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This document provides an overview of slope and how it is calculated and represented in algebra. It defines slope as rise over run and shows how to calculate it by counting squares between two points on a graph. Positive and negative slopes are introduced, as well as the slope-intercept form of a line, y=mx+b, where m is the slope and b is the y-intercept. Examples are given of calculating slope from points and graphing lines in slope-intercept form. Requirements for using the point-slope form, y-y1=m(x-x1), are also outlined.
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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.
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Slope-intercept form is represented by the equation y=mx+b, where m is the slope and b is the y-intercept. There are three methods to find the slope: rise over run, change in y over change in x, and point-slope formula. The slope tells the rate of change, while the y-intercept is the initial value when x=0. To graph a line in slope-intercept form, you plot the y-intercept and then use the slope to trace successive points on the line by calculating the rise over run at each interval. Word problems can be modeled using this form by identifying the independent and dependent variables and finding their relationship through calculating slope from ordered pairs of known values.
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This document provides an overview of slope and how it is calculated and represented in algebra. It defines slope as rise over run and shows how to calculate it by counting squares between two points on a graph. Positive and negative slopes are introduced, as well as the slope-intercept form of a line, y=mx+b, where m is the slope and b is the y-intercept. Examples are given of calculating slope from points and graphing lines in slope-intercept form. Requirements for using the point-slope form, y-y1=m(x-x1), are also outlined.
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The document discusses linear equations and slope. It covers plotting points on a coordinate plane, calculating slope using the rise over run formula, writing equations in slope-intercept form, finding the x- and y-intercepts, and graphing lines by making a table or using the slope and y-intercept. Methods are provided for determining the equation of a line given two points, the slope and one point, or from a graph.
slope_and_linear_eq--section_1.4.ppt
Slope describes the steepness of a line, with positive slope indicating a line rising from left to right and negative slope indicating a line falling from left to right. Slope is calculated as the rise over the run between two points and is commonly represented by m. There are several ways to find the equation of a line given certain information: if given the slope and y-intercept, the equation is y = mx + b; if given two points, slope is calculated as rise over run and then substituted into the point-slope form; if given the slope and one point, the point-slope form can be used. Horizontal lines have a slope of zero while vertical lines have undefined slopes.
1554 linear equations in two variables
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
Geo 3.6&7 slope
Reveiws slope from algebra I, then shows how to find lines parallel and perpendicular to a given line through a given point.
Geometry unit 3.7
The document discusses slopes and equations of lines. It defines slope as rise over run and provides formulas for calculating slope given two points on a line. It explains that the slope-intercept form is y=mx+b and point-slope form is y-y1=m(x-x1). Examples are given of writing equations of lines given slope and a point or y-intercept. Horizontal and vertical lines are also addressed.
Slope power point grade 8
Slope measures the steepness of a line and is calculated as the rise over the run between two points on the line. Slope is defined as the change in the y-values divided by the change in the x-values and is represented by the letter m. A line's slope does not change based on the two points used in the calculation. Vertical lines have undefined slopes, horizontal lines have a slope of zero, and all other non-vertical lines have a constant slope that can be found graphically, using a table, or using two points on the line.
Straight_Lines in mat 111 full lecture.ppt
A straight line is the shortest distance between two points. It can be defined using different forms of equations like slope-intercept, two point, and normal forms. The slope of a line is calculated as the tangent of the angle between the line and the x-axis. Parallel lines have equal slopes, while perpendicular lines have slopes that multiply to -1. A line's equation can be found using various properties like slope, two points on the line, or intercepts with the axes.
Slope intercept intro
The document discusses the slope-intercept form of equations of lines. It explains that the slope-intercept form can be written as y = mx + b, where m is the slope and b is the y-intercept. The slope represents how fast the line rises or falls, and the y-intercept is where the line crosses the y-axis. Some examples of lines in slope-intercept form are worked out, identifying the slope and y-intercept in each case.
TechMathI - Slope intercept form
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.
Linear functions
A linear function is an equation of the form y = mx + b, where m is the slope and b is the y-intercept. The slope is defined as the ratio of the rise over the run between any two points on the line. Lines with the same slope are parallel, while lines with slopes that are negative reciprocals of each other are perpendicular. There are also horizontal and vertical lines, where horizontal lines have a slope of 0 and vertical lines have an undefined slope. The point-slope form of a line is used to find the equation of a line given a point and the slope.
What is Slope?
This is a presentation for a teach lecture that explains what slope is and the three methods you can use to find it. Also includes a Khan Academy video explaining slope.
February 18 2016
The document discusses various formulas used to represent lines in the coordinate plane, including:
- Slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
- Point-slope form: y – y1 = m(x – x1), where (x1, y1) is a known point on the line and m is the slope.
- Standard form: Ax + By = C, where A, B, and C are constants and A and B cannot both be 0.
It provides examples of writing equations of lines in different forms given information like the slope, a point, or the graph of the line. Converting between
Graphing, Slope, And Special Lines
This document discusses graphing linear equations and determining slope. It provides examples of graphing lines with given equations like y = 2x - 4 and finding the slopes between points. Special lines like horizontal and vertical lines are examined, where horizontal lines have a slope of 0 and vertical lines are undefined. Pairs of lines are graphed and observed to have the same or opposite slopes based on their equations. In conclusion, the slope is important in graphing linear equations and representing the steepness of inclined lines.
@ Business Mathematics Chapter 1& 2.pptx
This document provides an overview of the course "Business Mathematics" which covers topics like linear equations, nonlinear equations, and economic applications of linear and quadratic models. The course is targeted at second year ABVM students.
Unit one discusses linear equations, their basic concepts and properties. It also covers developing linear equations using the slope-intercept form, slope-point form, and two-point form. Nonlinear equations are defined as equations with terms of degree two or higher that do not represent straight lines.
Economic applications of linear and quadratic models are also discussed. Functions and curves are defined in economics, with examples like the relationship between money earned and hours worked given as a simple linear function.
Similar to Algebra 1 power pointlr (20)
Algebra 1 power pointlr
- 1. Algebra 1 Chapter 5
- 2. Slope Slope is represented by the letter m Rise Run Slope =
- 3. Where can slope be found in the world?
- 4. Construction
- 5. Recreation
- 6. Sports
- 7. Engineering
- 8. Quick Reminder Lines rising from left to right have a positive slope
- 9. Lines falling from left to right have a negative slope
- 10. 0 slope
- 12. Finding Slope by counting squares run rise Rise= 3 Run= 2 3 2 Slope=
- 13. Practice What is the slope? Find the slope by counting rise over run.
- 14. Answer to practice run rise 3 1 Slope= or 3
- 15. More Practice What is the slope? Count rise over run.
- 16. Answer 5 4 Slope= -
- 17. Calculating slope Requires two points (x ,y ) (x ,y ) m= 2 2 1 1 y - y x - x 2 1 2 1
- 18. Example (3, -2) (1, -4) y -y (x ,y ) (x ,y ) -4-1 1-3 -5 -2 5 2 1 2 1 1 2 2 = = x - x (3 , -2) (1 , -4) 1 2
- 19. Slope Intercept Form y= mx+b m= slope b= y intercept slope y intercept
- 20. y intercept The y intercept is where the line crosses the y axis. y axis y intercept y intercept = 2 x axis
- 21. y intercept y intercepts can be positive or negative numbers y axis x axis y intercept= +1 y axis x axis y intercept= -2
- 23. Graphing Slope Intercept Form Step one: graph y intercept on y axis Step two: from that point use slope to graph second point Step three: connect the points You have now graphed a line using slope-intercept form.
- 26. Point-slope Form y- y = m(x-x ) 1 1
- 27. Point slope form requirements You must have one point and the slope of the line in order to write in point-slope form. You then substitute the slope in for the letter m and the numbers from the point in there correct spot.
- 29. Prentice Hall Algebra I Volume 1 Teacher’s Edition Pearson Education Inc., 2011 (p.311). Prentice Hall Algebra I Volume I Teacher’s Edition Teacher Resources Chapter 5, Pearson Education Inc., 2011 (Practice Forms) This citation is for slides (8-28). I