1. Warm Up Find each y-intercept. 1. y = 3x + 2 2. 5x – 3y = 12
Find each slope.
x + 2y = 6 3.
Write this equation in y=mx+b form.
5. 4x + 2y = 10

2. Writing Equations of Parallel and Perpendicular Lines

3. Writing an equation in Slope intercept form (y=mx+b) given a slope and the y-intercept
Example 1: Example 2:
Given:
slope = 1; y-intercept = 0
Given:
rate of change = 0; y-intercept = -5

4. Writing an equation in Point-slope form given a slope and the y-intercept
Examples :
Write an equation in point-slope form for the line with the given slope that contains the given point. A. B. C.
m = -2 and b = 3
m = 3/2 and
m = 1 and ( 0 , -4 )

5. Remember from y=mx+b, we need a slope and a y intercept.
What happens when we may know the slope,
but we do not know the y - intercept?
Well…If we know a SLOPE and a POINT
that the graph passes through, we can use ….
POINT-SLOPE FORMULA!

6. Writing an equation in Slope intercept form given 2 points
Example 9:
Write the equation that describes the line in slope-intercept form. Remember, we need an m and a b! Hint: Find slope first…Then use Point slope formula!
( 5 , 7 ) , ( 6 , 8 )

7. Writing an equation in Slope intercept form given a slope and a point
Example 5:
Write the equation that describes the line in slope-intercept form.
m = ¾ , ( -4 , -1 )

8. Let’s recall what we know about parallel and perpendicular lines…

9. Parallel Lines Perpendicular Lines SAME SLOPE but Different
y-intercept
y = 2x y = 3+2x
m = m = 2
Slopes are NEGATIVE
RECIPROCALS
y = 2x y = 3 - ½x
m = m = - ½
Horizontal Lines are parallel
y = y = 8
m = m = 0
Vertical and Horizontal Lines are perpendicular to each other
y = x = 1
m = m = undefined
Vertical Lines are parallel
x = x = -4
m = undefined m = undefined

10. Example 1
Write the equation of the line with a y-intercept of -2 and parallel to y = 4/5x.
Step 1 Find the slope of the new line.
Step 2 Write the equation in slope-intercept form using y = mx + b or y – y1 = m(x – x1)

11. Example 2
Write the equation of the line with a y-intercept of 4 and perpendicular to y = 2x + 1.
Step 1 Find the slope of the new line.
Step 2 Write the equation in slope-intercept form using y = mx + b or y – y1 = m(x – x1)

12. Example 3
Write an equation in slope-intercept form that is perpendicular to the graph and has a
y-intercept of -3. y x 7 6 5 4 3 2 1 −1 −6 −5 −4 −3 −2

13. Example 4
Write an equation in slope-intercept form for the line that passes through (4, 10) and is parallel to the line described by y = 3x + 8.
Step 1 Find the slope of the new line.
Step 2 Write the equation in slope-intercept form using y = mx + b or y – y1 = m(x – x1)

14. Example 5
Write an equation in slope-intercept form for the line that passes through (2, –1) and is perpendicular to the line described by y = 2x – 5.
Step 1 Find the slope of the new line.
Step 2 Write the equation in slope-intercept form using y = mx + b or y – y1 = m(x – x1)