1. Slope-Intercept Form

2. Slope

3. Key Terms
Slope – The ratio between the amount of rise to the amount of “run”. The rate of change of a line.
Y-Intercept – The point where a line crosses the y-axis on a coordinate plane. (x = 0 at this point) 3

4. Slope-Intercept Form of a Line
A linear equation is in slope-intercept form when it has the form:
y = mx + b, where m is the slope and b is the y-intercept.
y-intercept
slope
y = mx + b

5. Identify slope & y-intercept
y = 3x y = -2x + 4
y = ¾ x – y = -4x
5. y = 5

6. Can you find the slope & y-intercept?
3x + 7y = -9

7. Converting to Slope-Intercept
Solve the equation for y.
15x + 3y = 9
3y = -15x + 9
y = -5x + 3
Subtract 15x from both sides.
-15x x
Divide each term by 3.
m = -5; b = 3

8. You Try:
1. 8x – 2y = x + 3y = 15

9. Graph Using Slope-Intercept
y = -5x + 3
m = -5 (slope); b = 3 (y-intercept)
Step 1: Graph the y-intercept.
Step 2: Slope is rise over run. -5 =
Step 3: From y-intercept, go down 5, right 1 and graph 2nd point. Draw a line connecting the two points.

10. You Try:
y = 4x – y = 6x + 5

11. Guided Practice: p #1-11
Assignment:

12. Parallel Lines Parallel lines never intersect.
Parallel lines have slopes that are equal (the same).

13. Example: Given: y = 3x -7 and y = 3x + 10 Find the slope of each.
Both have a slope of 3.
Therefore, the two lines are parallel.

14. Determine which of the functions represent parallel lines.
(Hint: Rewrite each function in slope-intercept form.)
2x + 4y = 10
6x – 3y = -24
10x + 5y = -20
d. -16x + 8y = -56

15. Perpendicular Lines Perpendicular lines intersect at a right angle.
The slopes of perpendicular lines are negative reciprocals of each other.
Their product is -1.

16. Example: Given: y = ⅓x – 4 and y = -3x + 8
⅓ and -3 are negative reciprocals.
(⅓)(-3) = -1.
Therefore, the two lines are perpendicular.

17. Determine which two lines are perpendicular.
(Hint: Rewrite each equation in slope-intercept form.)
-12x + 6y = -24
-8x + 2y = -6
16x + 4y = 8
3x + 12y = 84

18. Guided Practice: p. 31 #12
Assignment: