TechMathI - Slope intercept form
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This document discusses linear equations and slope-intercept form. It provides examples of: 1) Finding the slope and y-intercept of linear equations in slope-intercept form like y = 4x + 2. 2) Writing equations of lines given the slope and y-intercept, such as an equation with m = 3 and y-intercept of 7. 3) Finding the slope and y-intercept from two points on a line, then writing the equation in slope-intercept form.
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2. It provides examples of writing equations in each form given specific information like two points, an x-intercept and y-intercept, a point and slope, or just a slope and y-intercept.
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4) Given an equation and a point that the line passes through, solve for the missing slope (m) or y-intercept (b) value.
identities1.2
The document discusses the concept of slope and how it is used to describe the steepness of a line. It defines slope as the ratio of the vertical change (rise) to the horizontal change (run) between two points on a line. Several forms of linear equations are presented, including point-slope form, slope-intercept form, and standard form. Relationships between parallel and perpendicular lines based on their slopes are also described. Examples are provided to demonstrate finding slopes, writing equations of lines, and determining if lines are parallel or perpendicular based on their slopes.
Graphing lines using slopeintercept
This document provides information about graphing lines using slope-intercept form. It defines slope-intercept form as y=mx+b, where m is the slope and b is the y-intercept. It shows how to find the slope and y-intercept from linear equations in various forms and how to write equations in slope-intercept form. It also demonstrates how to graph lines by plotting points using the slope and y-intercept. Key steps for graphing include finding the slope and y-intercept, plotting the y-intercept, using the slope to determine other points, and drawing the line through the points. The document also discusses parallel lines as those with the same slope.
5.5 parallel perp lines
The document discusses point-slope form and writing linear equations. It provides examples of writing equations for lines that are parallel and perpendicular to given lines. Specifically, it explains that parallel lines have the same slope and different y-intercepts, while perpendicular lines have slopes that are negative reciprocals of each other. Examples are given of writing equations for parallel and perpendicular lines using point-slope form based on a given point and the slope of another line.
6.2-3 Slope-Intercept and Standard forms
This document provides instruction on writing and graphing linear equations in slope-intercept and standard form. It includes examples of finding the slope and y-intercept from an equation in slope-intercept form, writing an equation given the slope and y-intercept, graphing lines from their equations, finding x- and y-intercepts to graph in standard form, and transforming between the two forms. Students are provided practice problems to complete for homework.
5.1 writing linear equations day 1
This chapter discusses writing linear equations in slope-intercept form (y=mx+b) by either knowing the slope and y-intercept or by being given two points on the line. It provides examples of writing equations of lines from graphical representations or when given the slope and y-intercept numerically. Students are guided in writing linear equations from different scenarios like being given two points or the cost equation of a recording studio based on hours of studio time.
Algebra 2 Section 1-4
This document provides instruction on writing linear equations in slope-intercept form, point-slope form, and finding equations of lines parallel or perpendicular to given lines. It defines key vocabulary like slope, parallel, and perpendicular. Examples are worked through, like writing the equation of a line given its slope and a point, or finding the equation of a line perpendicular to another line passing through a given point. The problem set provided practices writing various linear equations.
4 6 equations of lines
The document discusses equations of lines. It introduces the linear equation y = 2x - 1 and shows how to graph it by substituting values for x and finding the corresponding y-values. This forms the line's points (ordered pairs). It explains that a linear equation can be written in the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept. It provides examples of writing equations from their graphs in slope-intercept form and graphing lines from equations written in this form by using the slope and y-intercept. Finally, it gives examples of writing equations of lines parallel or perpendicular to given lines that pass through a given point.
Topic 8 (Writing Equations Of A Straight Lines)
The document provides information on properties of straight lines and methods to write equations of straight lines given different conditions. It also discusses solving systems of linear equations using different methods like graphing, substitution, elimination and Cramer's rule. Key points covered include writing equations in slope-intercept and standard form, finding slopes of parallel and perpendicular lines, and properties of consistent, inconsistent and dependent systems of linear equations.
2.4 writing equations of lines
1) This document discusses writing linear equations in slope-intercept form (y=mx+b) given different information: the slope (m) and y-intercept (b), a graph, the slope and a point, or two points.
2) It provides examples of writing equations of lines given: the slope and y-intercept, a graph, the slope and a point, two points, or the x- and y-intercepts.
3) The key steps are to identify the slope (m) and y-intercept (b) from the information provided, then substitute those values into the slope-intercept form equation to write the linear equation.
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The document discusses finding the x-intercept and y-intercept of linear equations by setting either x or y equal to 0 and solving for the other variable. It provides examples of finding the intercepts of equations and graphing the resulting point coordinates. Students are asked to practice finding and graphing intercepts for several equations.
TechMathI - Rate of change and slope
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This document contains a 36 question multiple choice test on various math concepts including:
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This document contains 30 math word problems testing foundations concepts like rates, proportions, percentages, and percent change. The problems can be solved by setting up and solving proportions, finding unit rates, calculating percentages, or determining percent change between two amounts. Key information includes rates, costs, percentages, initial and final amounts, and measurements involved in rate and percent problems.
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Similar figures are two-dimensional shapes that have the same shape but can differ in size. To be similar, the corresponding sides of the figures must be proportional, meaning they differ by a constant scale factor. Similar figures have the same angle measures but different side lengths. Problems involving similar figures can be solved by identifying the scale factor between corresponding sides and using proportional reasoning.
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This document contains 4 math word problems involving similar triangles and scaling factors to determine unknown side lengths or heights. It also provides examples of finding the height of objects like trees using the similarity of triangles formed by shadows of objects of known height.
TechMathI - 6.1 - Ratio and Proportion
1. The document provides examples of ratios, proportions, rates, unit rates, and examples of setting up and solving proportions using cross multiplication.
2. It includes multi-step proportion examples involving fractions with variables in both the numerator and denominator.
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This document contains a 33 question test on polygons and their properties. The test covers identifying polygons by name and type, finding missing side lengths and angle measures of polygons, calculating sums of interior and exterior angles, determining which statements about polygon properties are true or false, and identifying polygons based on given properties. The test includes multiple choice, true/false, and short answer questions.
TechMathI - Ch5 Vocab Quiz
This document is a vocabulary quiz that tests knowledge of polygon terms. It contains 17 multiple choice questions that ask the learner to match polygon names like triangle, square, pentagon, and hexagon with their definitions relating to number of sides, side properties, angles, and geometric shapes. The word bank at the bottom provides additional polygon shape names as potential answers.
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This document discusses properties and definitions related to trapezoids. It defines a trapezoid as a quadrilateral with one pair of parallel sides, and defines an isosceles trapezoid as one where the non-parallel sides are congruent. It states that the diagonals of an isosceles trapezoid are congruent and that the median of any trapezoid is parallel to the bases and has a length that is half the sum of the base lengths. It includes examples of finding missing side lengths using the median property.
TechMathI - 5.5 - Special Parallelograms
1. The document discusses different types of quadrilaterals including trapezoids, parallelograms, rectangles, squares, and rhombuses.
2. It provides steps to identify these shapes based on their properties like the number of parallel sides and whether the angles are right angles or the sides are congruent.
3. Tests are described to determine if a quadrilateral is a parallelogram based on properties like opposite sides being parallel and congruent.
TechMathI - 5.4 - Parallelograms
This document provides examples and practice problems for identifying angle measures in parallelograms. It gives the side lengths of parallelogram ABCD and asks to find the three other angle measures. It also provides a practice problem to find missing angle measures for an additional parallelogram.
TechMathI - 5.3 - Properties of Quadrilaterals
This document provides information about different types of quadrilaterals (four-sided polygons) through a foldable activity. It defines and lists properties of parallelograms, rectangles, rhombuses, squares, and trapezoids. Key quadrilaterals are distinguished by their parallel sides, right angles, and congruent sides or angles. The foldable allows students to draw and label examples of each quadrilateral type.
TechMathI - 5.2 - Angles of Polygons
This document contains information about polygons, including:
1. Formulas for calculating the sum of interior angles and exterior angles of polygons. The interior angle sum is (n-2)×180° and the exterior angle sum is 360°.
2. Examples of calculating interior and exterior angles for regular polygons with specific numbers of sides. Interior angles decrease and exterior angles increase as the number of sides increases.
3. Practice problems involving calculating unknown interior and exterior angles of polygons using the angle sum properties.
TechMathI - 5.1 - Polygons
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TechMathI - 4.5 - Altitudes, Medians, and Bisectors
This document provides information about medians, altitudes, and perpendicular bisectors of triangles:
1) A median is a line segment connecting a vertex to the midpoint of the opposite side. A triangle has 3 medians. The point where the 3 medians intersect is called the centroid.
2) An altitude is a line segment from a vertex perpendicular to the opposite side. It represents the "true height" of the triangle.
3) A perpendicular bisector is a line segment through the midpoint of a side, perpendicular to that side. The two segments formed on either side are congruent.
TechMathI - 4.2 - Proving Triangles Congruent
The document discusses three postulates for triangle congruence:
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2) Angle-Angle-Side (AAS) postulate - If two angles and a non-included side of one triangle are congruent to another, then the triangles are congruent.
3) Side-Side-Side (SSS) postulate - If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
TechMathI - 4.3 - Using Congruent Triangles
The document discusses three triangle congruence postulates:
1) Angle-Side-Angle (ASA) postulate states that if two angles and the included side of one triangle are congruent to another triangle, then the triangles are congruent.
2) Angle-Angle-Side (AAS) postulate states that if two angles and a non-included side of one triangle are congruent to another, then the triangles are congruent.
3) Side-Side-Side (SSS) postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
TechMathI - 4.4 - Isosceles and Right Triangle Theorems
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TechMathI - Slope intercept form
- 1. Bell Ringer Evaluate each expression. 1) .25x + 2 for x = 16 2) -2x – 5 for x = 3 Solve each equation for y. 3) y – 5 = 4x 4) 2y + 6 = -8x
- 2. What is a linear equation ? An equation whose graph is a line. Slope-Intercept Form
- 3. What is a y – intercept ? Where the line crosses the y – axis. Slope-Intercept Form y = m x + b where m = slope b = y-intercept
- 4. Slope-Intercept Form y = m x + b What is the slope and y-intercept of: y = 4x + 2 y = -2x - 1
- 5. What is the slope and y-intercept of: y = 3x – 5 y = -2x y = 4/5x + 5 You try!
- 6. Write an equation of the line with: m = 3 and y-intercept of 7 m = -1 and y-intercept of -2
- 8. (0,2) and (4,-1) y-intercept is 2
- 9. (-2,2) and (4, 4) y-intercept is -2
- 10. Find the slope given your two points. Then write an equation in slope-intercept form using the y-intercept. (-1,5) and (3,-3) y – intercept: 0 You try! (3,2) (4,6) y – intercept: 1
- 11. Graphing with slope-intercept form. y = 3x – 1 m = b = Your y-intercept can be written as an ordered pair.
- 12. Graphing with slope-intercept form. y = x – 3 m = b = You try! y = -1/2x + 2 m = b =
- 13. Homework