1. A 72 ft. pipe is cut into two pieces of lengths in a 5:7
ratio. What are the lengths of the two pieces?
2. A $40.00 shi...
Formulas:
The Slope of a Line:

The Slope Intercept Form:

The slope of the line passing
through the two points (x1,
y1) a...
Equations and their Graphs:

Equations of the form ax + by = c are called linear
equations in two variables.
y

Graph the ...
5
The slope of the line passing through the two
points (x1, y1) and (x2, y2) is given by the formula

y

(x2, y2)
y2 – y1
ch...
Example: Find the slope of the line passing
through the points (2, 3) and (4, 5).
Use the slope formula with x1= 2, y1 = 3...
The Slope Intercept Form of a Line:
A linear equation written in the form y = mx + b is in
slope-intercept form.
The slope...
Example: Graph the line y = 2x – 4.
1. The equation y = 2x – 4 is in the slope-intercept form.
So, m = 2 and b = - 4.
y
2....
The Slope Intercept Form of a Line:

Example 2: Graph the line 3y - 3x = 6.
Last Example: Graph the line -2x + y = -4.
slo...
Class Work:
See Handout
A linear equation written in the form y – y1 = m(x – x1)
is in point-slope form.
The graph of this equation is a line with...
Example: Write the slope-intercept form for the equation
of the line through the point (-2, 5) with a slope of 3.
Use the ...
Example: Write the slope-intercept form for the
equation of the line through the points (4, 3) and (2, 5).
5–3 =- 2 =- 1
m...
Two lines are parallel if they have the same slope.
If the lines have slopes m1 and m2, then the lines
are parallel whenev...
Two lines are perpendicular if their slopes are
negative reciprocals of each other.
If two lines have slopes m1 and m2, th...
• Linear Equations form straight lines. How do we
determine if an equation is linear?
It can be rewritten in the form: Ax ...
Class Work:
8-3: 28-36;
Plot & Label 3 points per problem
4.3-- All

20
January 9, 2014
January 9, 2014
January 9, 2014
Upcoming SlideShare
Loading in …5
×

January 9, 2014

1,061 views

Published on

Published in: Technology
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
1,061
On SlideShare
0
From Embeds
0
Number of Embeds
406
Actions
Shares
0
Downloads
9
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

January 9, 2014

  1. 1. 1. A 72 ft. pipe is cut into two pieces of lengths in a 5:7 ratio. What are the lengths of the two pieces? 2. A $40.00 shirt has been discounted 35%. What is the sale price of the shirt? 3. Find a number so that 20 more than one-third of the number equals three-fourths of that number. 4. x + 2 + x - 1 = 2 3 2 5. x + 3 = x - 2 6 4
  2. 2. Formulas: The Slope of a Line: The Slope Intercept Form: The slope of the line passing through the two points (x1, y1) and (x2, y2) is given by the formula A linear equation written in the form y = mx + b is in slope-intercept form.
  3. 3. Equations and their Graphs: Equations of the form ax + by = c are called linear equations in two variables. y Graph the equation 2x + 3y = 12. Find the x - intercept. Find the y-intercept. x -2 2 4
  4. 4. 5
  5. 5. The slope of the line passing through the two points (x1, y1) and (x2, y2) is given by the formula y (x2, y2) y2 – y1 change in y (x1, y1) x2 – x1 change in x x 6
  6. 6. Example: Find the slope of the line passing through the points (2, 3) and (4, 5). Use the slope formula with x1= 2, y1 = 3, x2 = 4, and y2 = 5. y2 – y1 5–3 m= = x2 – x1 4–2 2 =1 = 2 y (4, 5) 2 (2, 3) 2 x 7
  7. 7. The Slope Intercept Form of a Line: A linear equation written in the form y = mx + b is in slope-intercept form. The slope is m and the y-intercept is (0, b). To graph an equation in slope-intercept form: 1. Write the equation in the form y = mx + b. Identify m and b. 2. Plot the y-intercept (0, b). 3. Starting at the y-intercept, find another point on the line using the slope. 4. Draw the line through (0, b) and the point located using the slope. 8
  8. 8. Example: Graph the line y = 2x – 4. 1. The equation y = 2x – 4 is in the slope-intercept form. So, m = 2 and b = - 4. y 2. Plot the y-intercept, (0, - 4). x 3. The slope is 2. m = change in y 2 = 1 change in x 4. Start at the point (0, 4). (0, - 4) Count 1 unit to the right and 2 units up 1 to locate a second point on the line. The point (1, -2) is also on the line. (1, -2) 2 5. Draw the line through (0, 4) and (1, -2). 9
  9. 9. The Slope Intercept Form of a Line: Example 2: Graph the line 3y - 3x = 6. Last Example: Graph the line -2x + y = -4. slope intercept y = 2x - 4. When you know how to 'decode' the slope-intercept form, you won't have to make a table of x and y values any longer.
  10. 10. Class Work: See Handout
  11. 11. A linear equation written in the form y – y1 = m(x – x1) is in point-slope form. The graph of this equation is a line with slope m passing through the point (x1, y1). Example: The graph of the equation y 8 m=- y – 3 = - 1 (x – 4) is a line 2 of slope m = - 1 passing 2 through the point (4, 3). 4 1 2 (4, 3) x 4 8 14
  12. 12. Example: Write the slope-intercept form for the equation of the line through the point (-2, 5) with a slope of 3. Use the point-slope form, y – y1 = m(x – x1), with m = 3 and (x1, y1) = (-2, 5). y – y1 = m(x – x1) Point-slope form y – y1 = 3(x – x1) Let m = 3. y – 5 = 3(x – (-2)) Let (x1, y1) = (-2, 5). y – 5 = 3(x + 2) Simplify. y = 3x + 11 Slope-intercept form 15
  13. 13. Example: Write the slope-intercept form for the equation of the line through the points (4, 3) and (2, 5). 5–3 =- 2 =- 1 m= -2 – 4 6 3 y – y1 = m(x – x1) 1 (x – 4) 3 y = - 1 x + 13 3 3 y–3=- Calculate the slope. Point-slope form Use m = - 1 and the point (4, 3). 3 Slope-intercept form 16
  14. 14. Two lines are parallel if they have the same slope. If the lines have slopes m1 and m2, then the lines are parallel whenever m1 = m2. y (0, 4) Example: The lines y = 2x – 3 y = 2x + 4 and y = 2x + 4 have slopes m1 = 2 and m2 = 2. x y = 2x – 3 The lines are parallel. (0, -3) 17
  15. 15. Two lines are perpendicular if their slopes are negative reciprocals of each other. If two lines have slopes m1 and m2, then the lines are perpendicular whenever y 1 m2= or m1m2 = -1. y = 3x – 1 m1 (0, 4) Example: The lines y = 3x – 1 and 1 y = - x + 4 have slopes 3 m1 = 3 and m2 = -1 . 3 1 y=- x+4 3 x (0, -1) The lines are perpendicular. 18
  16. 16. • Linear Equations form straight lines. How do we determine if an equation is linear? It can be rewritten in the form: Ax + By = C This is the Standard Form of a linear equation where: a.) A and B are not both zero. b.) The largest exponent is not greater than 1 Determine Whether the Equations are Linear: 1. 4 - 2y = 6x 2. -4/5x = -2 3. -6y + x = 5y - 2 Remember: This is to determine whether an equation is linear (forms a straight line) or not. The standard form is also used to determine x and y intercepts.
  17. 17. Class Work: 8-3: 28-36; Plot & Label 3 points per problem 4.3-- All 20

×