Download y-intercept - Humble ISD

Warm Up
Find each y-intercept.
1. y = 3x + 2
2. 5x – 3y = 12
Find each slope.
3.
4.
Write this equation in y=mx+b form.
5. 4x
+ 2y = 10
6x + 2y = 6
Writing Equations of
Parallel and
Perpendicular Lines
Writing an equation in Slope intercept form (y=mx+b)
given a slope and the y-intercept
Example 1:
Given:
slope = 1; y-intercept = 0
Example 2:
Given:
rate of change = 0; y-intercept = -5
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.
m = -2 and b = 3
m = 3/2 and
C.
m = 1 and ( 0 , -4 )
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!
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)
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 )
Let’s recall what we know about parallel and
perpendicular lines…
Parallel Lines
SAME SLOPE but Different
y-intercept
y = 2x+1
y = 3+2x
m=2
m=2
Perpendicular Lines
Slopes are NEGATIVE
RECIPROCALS
y = 2x+1
y = 3 - ½x
m=2
Horizontal Lines are parallel
y = -2
y=8
m=0
m=0
Vertical Lines are parallel
x=3
x = -4
m = undefined m = undefined
m=-½
Vertical and Horizontal Lines are perpendicular
to each other
y = -4
x=1
m = 0 m = undefined
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)
Example 2
Write the equation of the line with a yintercept 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)
Example 3
Write an equation in slope-intercept form that is
perpendicular to the graph and has a
y-intercept of -3.
y
7
6
5
4
3
2
1
x
6
5
4
3
2
1
1
1
2
3
4
5
6
2
3
4
5
6
7
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)
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)