1. Slope-Intercept Form
Section 5-3 Part 1

2. Goals
Goal
Rubric
To write linear equations using slope-intercept form.
Level 1 – Know the goals.
Level 2 – Fully understand the goals.
Level 3 – Use the goals to solve simple problems.
Level 4 – Use the goals to solve more advanced problems.
Level 5 – Adapts and applies the goals to different and more complex problems.

3. Vocabulary Parent Function Linear Parent Function Linear Equation
y-intercept
Slope-Intercept Form

4. Definition
Family of Functions - is a set of functions whose graphs have basic characteristics in common.
Example: All linear functions form a family because all of their graphs are the same basic shape, a line.
Parent Function – is the simplest or basic function within a family of functions.
Linear Parent Function – is y = x or f(x) = x.

5. Definition
Linear Equation - is an equation that models a linear function.
In a linear equation the variables are raised to the 1st power only.
Example:
Linear equation; y = 2x + 3.
Not a linear equation; y = x2 or y = 2x.
The graph of a linear equation contains all the ordered pairs that are solutions of the equation.
y-intercept – is the y-coordinate of the point where the line crosses the y-axis.

6. Slope-Intercept Form of a Linear Equation
If you know the slope of a line and the y-intercept, you can write an equation that describes the line.
Step 1 If a line has a slope of m and the y-intercept is b, then (0, b) is on the line. Substitute these values into the slope formula.

7. Slope-Intercept Form of a Linear Equation
Step 2 Solve for y:
Simplify the denominator.
Multiply both sides by x.
+b b
mx = y – b
Add b to both sides.
mx + b = y, or y = mx + b

8. Slope-Intercept Form of a Linear Equation
y = mx + b
slope
y-intercept
Any linear equation can be written in slope-intercept form by solving for y and simplifying. In this form, you can immediately see the slope and y-intercept. Also, you can quickly graph a line when the equation is written in slope-intercept form.

9. Finding the Slope and y-intercept of a Line
Procedure for finding the slope and y-intercept of a line.
Rewrite the equation of the line in slope-intercept form by solving for y.
The coefficient of x, is the slope and the constant term, is the y-intercept.
y = mx + b
Slope (always comes in front of x!)
y – intercept (where the line crosses the y-axis)

10. Example: Finding the Slope and the y-Intercept
Find the slope and the y-intercept of the line whose equation is 2x – 3y + 6 = 0.
Procedure We need to solve for y.
This is the given equation.
2x – 3y + 6 = 0
To isolate the y-term, add 3 y on both sides.
2x + 6 = 3y
Reverse the two sides. (This step is optional.)
3y = 2x + 6
Divide both sides by 3.
The coefficient of x, 2/3, is the slope and the constant term, 2, is the y-intercept.

11. Example: Find the slope and y-intercept of the equation.
(c) x = -2
(b) y = 3
m = undefined
b = none
(a) y = ½ x + 5
y = mx + b
y = mx + b
y = 0x + 3
m = ½
b = 5
m = 0
b = 3

12. Example: Find the slope and y-intercept of the equation.
d) 2x – 3y = 18
m = 2/3
b = - 6
y = mx + b
Solve for y.
y = 2/3 x - 6
2x – 3y = 18
– 3y = 18 – 2x
y = /3 x
y = 2/3 x - 6

13. Your Turn: Find the slope and y-intercept of the equation.
1) 3y + 12 = 6x
2) 3y – x = 12
Solve for y.
Solve for y.
3y = 6x – 12
3y = x + 12
y = 2x – 4
y = 1/3 x +4
y = mx + b
y = mx + b
y = 2x – 4
y = 1/3 x + 4
m = 2
b = –4
m = 1/3
b = 4

14. Your Turn: 1. y = -x + 8 2. x + 4y = 24 m = b = m = b =-1 8
-1/4 6 -1
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15. Example: Write the equation of the line in slope-intercept form.
slope = ; y-intercept = 4
y = mx + b
Substitute the given values for m and b.
y = x + 4
Simplify if necessary.

16. Example:
Write the equation that describes the line in slope-intercept form.
slope = –9; y-intercept =
y = mx + b
Substitute the given values for m and b.
y = –9x +
Simplify if necessary.

17. Your Turn:
Write the equation that describes the line in slope-intercept form.
slope = 3; y-intercept =
y = mx + b
Substitute the given values for m and b.
Simplify if necessary.

18. Your Turn:
Write the equation that describes the line in slope-intercept form.
slope = ; y-intercept = –6
y = mx + b
Substitute the given values for m and b.
Simplify if necessary.

19. Example: Writing Linear Equations in Slope-Intercept Form
Write the equation that describes the line in slope-intercept form.
slope = 2; (3, 4) is on the line
Step 1 Find the y-intercept.
y = mx + b
Write the slope-intercept form.
4 = 2(3) + b
Substitute 2 for m, 3 for x, and 4 for y.
–2 = b
4 = 6 + b
–6 –6
Solve for b. Since 6 is added to b, subtract 6 from both sides to undo the addition.

20. Example: Continued Step 2 Write the equation. y = mx + b y = 2x + (–2)
slope = 2; b = - 2
Step 2 Write the equation.
y = mx + b
Write the slope-intercept form.
y = 2x + (–2)
Substitute 2 for m, and –2 for b.
y = 2x – 2

21. Your Turn:
A line has a slope of 8 and (3, –1) is on the line. Write the equation that describes this line in slope-intercept form.
Step 1 Find the y-intercept.
y = mx + b
Write the slope-intercept form.
–1 = 8(3) + b
Substitute 8 for m, 3 for x, and –1 for y.
–25 = b
–1 = 24 + b
–24 –24
Solve for b. Since 24 is added to b, subtract 24 from both sides to undo the addition.

22. Continued Step 2 Write the equation. y = mx + b y = 8x + (–25)
slope = 8; b = - 25
Step 2 Write the equation.
y = mx + b
Write the slope-intercept form.
y = 8x + (–25)
Substitute 8 for m, and –25 for b.
y = 8x – 25

23. Example: Writing an Equation From a Graph
Find the linear equation of the line shown on the graph.
y-intercept = 4 y • •
Rise = –2
Step 1 Pick two points on the line and determine the slope of the line from the graph. • •
m =
Run = 5
Step 2 Find the y-intercept from the graph.
b = 4
Step 3 Write the linear equation in slope-intercept form (y = mx+ b).

24. Your Turn: y = –x + 2 y = 2x – 2 Write the equation of the line shown.B. A.
y = –x + 2
y = 2x – 2

25. Example: Write an Equation From Two Points
What equation in slope-intercept form represents the line that passes through the points (2, 1) and (5, -8).
Step 1 Use the two points to find the slope.
Step 2 Use the slope and one of the points to find b.
Step 3 Substitute the slope and y-intercept into the slope-intercept form (y = mx + b).

26. Your Turn:
What equation in slope-intercept form represents the line that passes through the points (1, -6) and (-3, 10).
Step 1 Use the two points to find the slope.
Step 2 Use the slope and one of the points to find b.
Step 3 Substitute the slope and y-intercept into the slope-intercept form (y = mx + b).

27. Your Turn:
What equation in slope-intercept form represents the line that passes through the points (3, -2) and (1, -3).
Step 1 Use the two points to find the slope.
Step 2 Use the slope and one of the points to find b.
Step 3 Substitute the slope and y-intercept into the slope-intercept form (y = mx + b).

28. Joke Time Why shouldn’t you write with a broken pencil?
Because it is pointless!
What do you call a man with no arms and no legs playing in the leaves?
Russell!
Which side of a cheetah has the most spots?
The outside.

29. Assignment
5-3 Part 1 Exercises Pg : #6 – 40 even