1. Write an equation of a line with
slope 4 and y-intercept at (0, -3)
2. Write 12 – y = 2x – 5 in slopeintercept form. What are the slope
and y-intercept?
3. Find perpendicular slope to
(-2, 3) & (4, -5)
1.
2.
y = 4x - 3
12 – y = 2x - 5
-12
-12
-y = 2x – 17
-1 -1 -1
y = -2x + 17
slope = -2
y-int: (0, 17)
3.
(-2, 3) & (4, -5)
(x1, y1) & (x2, y2)
𝒚𝟐 − 𝒚𝟏
−𝟓 − 𝟑
−𝟖
𝟒
𝑚=
=
=
=−
𝒙𝟐 − 𝒙𝟏 𝟒 − (−𝟐)
𝟔
𝟑
Perpendicular Slope =
𝟑
𝟒
Thurs
9/24
Learning Objective:
To write an eq’n of a line
given slope & a point
Lesson Hw: Pg. 86 # 11 – 25 odd,
2–4
32 – 35, *9, *45 CC
Fri
9/25
Learning Objective:
To remember everything
from 2.1 – 2.4
Lesson Hw: 2.1 – 2.4 Review WS
Rev
Algebra II
 To
write an equation of a line
given its slope and a point on the
line
 Slope-Intercept
Form
𝑦 = 𝑚𝑥 + 𝑏
Use to write an equation of a line
when given the slope m and the
y-intercept b
 Point-Slope
Form
𝑦 − 𝑦1 = 𝑚 𝑥 − 𝑥1
Use to write an equation of a line
when given a point (x1, y1) and
slope m
*May need to find slope if given two
points, then use point-slope form to
write the linear equation
 Standard
Form
𝐴𝑥 + 𝐵𝑦 = 𝐶
A, B, C are integers (no fractions)
 Parallel
slope
Lines – have the same
 Perpendicular
Lines – have
opposite reciprocal slopes
1. A line passes through (-5, 2)
3
.
5
with slope What is the equation
of the line in point-slope form?
𝑦 − 𝑦1 = 𝑚 𝑥 − 𝑥1
3
𝑦 − 2 = 𝑥 − −5
5
3
𝑦−2= 𝑥+5
5
2. A line passes through (7, -1)
with slope -3. What is the equation
of the line in point-slope form?
𝑦 − 𝑦1 = 𝑚 𝑥 − 𝑥1
𝑦 − −1 = −3 𝑥 − 7
𝑦 + 1 = −3 𝑥 − 7
3. A line passes through (3, 2) and
(5, 8). What is the equation of the
line in point-slope form?
* Find Slope
𝒚𝟐 − 𝒚𝟏 𝟖 − 𝟐 𝟔
𝑚=
=
= =𝟑
𝒙𝟐 − 𝒙𝟏 𝟓 − 𝟑 𝟐
** Use the slope and EITHER point.
𝑦 − 𝑦1 = 𝑚 𝑥 − 𝑥1
y – 2 = 3(x – 3) or y – 8 = 3(x – 5)
4. A line passes through (-5, 0) and
(0, 4). What is the equation of the line
in point-slope form?
* Find Slope
𝒚𝟐 − 𝒚𝟏
𝟎−𝟒
−𝟒 𝟒
𝑚=
=
=
=
𝒙𝟐 − 𝒙𝟏 −𝟓 − 𝟎 −𝟓 𝟓
** Use the slope and EITHER point.
𝑦 − 𝑦1 = 𝑚 𝑥 − 𝑥1
𝟒
𝟒
y – 0 = (x –(-5)) or y – 4 = (x – 0)
y
𝟓
𝟒
= (x
𝟓
+5)
or
𝟓
y–4=
𝟒
x
𝟓
5. Using #4, what is the equation
of the line in slope-intercept form?
𝟒
𝟓
* We know the slope is
** We know the y-intercept is (0, 4)
y = mx + b
y=
𝟒
x
𝟓
+4
6. Using #4 & #5, what is the
equation of the line in standard
form?
*We know the slope-intercept form
𝟒
is
y= x+4
𝟓
𝟒
=( x
𝟓
(5) y
+ 4)(5)
5y = 4x + 20
-4x -4x
-4x + 5y = 20 or 4x – 5y = -20
7. What is the equation of a line
parallel to y = 6x – 2 that goes
through (1, -3) in slope-intercept
form?
*Parallel lines have same slope, so
m=6
y – (-3) = 6(x – 1)
y + 3 = 6x – 6
-3
-3
y = 6x - 9
8. What is the equation of a line
perpendicular to y = -4x + 1 that
goes through (8, 5) in slope-intercept
form?
*Perpendicular lines have opposite
1
reciprocal slopes, so m =
y–5=
y-5=
+5
1
(x – 8)
4
1
x-2
4
4
+5
y=
1
x
4
+3
9. What is the equation of a line
parallel to 4x + 2y = 7 that goes
through (4, -2) in standard form?
*Find slope of original line
4x + 2y = 7
-4x
-4x
2y = -4x + 7
2
2
2
y = -2x +
7
2
Slope = -2
9. Slope = -2, Goes through (4, -2)
in standard form?
Start with
y – (-2) = -2(x – 4) point slope
form
y + 2 = -2x + 8
-2
-2
Slopeintercept
y = -2x + 6
form!
+2x +2x
End with
2x + y = 6
standard
form!
If you have a point and the slope,
Then you can find point-slope form
y + 2 = -2(x – 4)
Then you can find slope-intercept form
y = -2x + 6
Then you can find standard form
2x + y = 6
10. Using #9, write an equation of a line
perpendicular to 4x + 2y = 7 in standard
form.
Slope = -2
Goes through (4, -2)
1
perpendicular slope =
2
1
1
y – (-2) = (x – 4)
y+2= x-2
2
2
-2
-2
1
y= x-4
2
1
(2)y = ( x – 4)(2)
2y = x – 8
2
-x -x
-x + 2y = -8
or x – 2y = 8
11. What is the equation of a line
perpendicular to -2x + 3y = - 3
and goes through (0, 6) in slopeintercept form?
Perpendicular
-2x + 3y = - 3
3
slope = −
+2x
+2x
2
3y = 2x – 3
3
y=− 𝑥+6
3
3 3
2
2
y= 𝑥−1
3
12.
– 4x + 6y = 12
x-intercept (y = 0)
– 4x + 6(0) = 12
– 4x = 12
x = –3
(–3, 0)
y-intercept (x = 0)
–4(0) + 6y = 12
6y = 12
y=2
(0, 2)
 Each
interval is one unit
 Write an equation for the line
shown.
(All 3 forms)
 *Hint: what do
You know from
The graph?
Which form of equation can
you use with the info?