Mr. Sims
Standard Form: Ax + By = C
Slope-Intercept Form: y = mx + b
Point-Slope Form: y – y1 = m(x – x1)
Algebra 2
Section 9.3 B
Equation of a Line
A line has the given slope, y-intercept, or contains the indicated
points. Write an equation, in standard form, of each line.
(x1,y1) (x2,y2)
1. (-1,3) , (0,4)
y y
m
2
1
x x
2
1
43
m
0  (1)
find slope 1st
(x1,y1)
(0,4) , m = 1
y – y1 = m(x – x1)
y – 4 = 1(x – 0)
y–4=x
-y
point-slope form
-y get in standard form {Ax + By = C}
x–y=-4
1

1
m=1
substitute slope with either
point into point-slope form
{try to stay away from negatives}
Mr. Sims
Standard Form: Ax + By = C
Slope-Intercept Form: y = mx + b
Point-Slope Form: y – y1 = m(x – x1)
(x1,y1) (x2,y2)
2. (2,-3) , (0,4)
y y
m
2
find slope 1st
x x
2
m
1
(x1,y1)
1
4  (3)
02
7
m
2
substitute slope in with
either point into point-slope form
{try to stay away from negatives}
7
(0,4) , m  
2
y – y1 = m(x – x1)
point-slope form
7
y  4   (x  0)
2
7
2 y  4  x
2
get in standard form
clear out fraction 1st
2y – 8 = -7x
-2y
-2y
-7x – 2y = -8
Mr. Sims
Standard Form: Ax + By = C
Slope-Intercept Form: y = mx + b
Point-Slope Form: y – y1 = m(x – x1)
(x1,y1) (x2,y2)
3. (7,3) , (-3,6)
y y
m
2
1
x x
2
find slope 1st
1
63
m
37
3
m
10
(x1,y1)
3
(7,3) , m  
10
y – y1 = m(x – x1)
3
-10 y  3   (x  7)
10
-10y + 30 = 3(x – 7)
-10y + 30 = 3x – 21
-3x
-30
point-slope form
get in standard form
clear out fraction 1st
distributive property
-3x -30
-3x – 10y = -51
substitute slope in with
either point into point-slope form
{try to stay away from negatives}
Mr. Sims
Standard Form: Ax + By = C
Slope-Intercept Form: y = mx + b
Point-Slope Form: y – y1 = m(x – x1)
(x1,y1) (x2,y2)
4. (7,5) , (-3,5)
(x1,y1)
y y
m
2
1
x x
2
find slope
1st
1
55
m
37
(7,5) , m = 0
y – y1 = m(x – x1) point-slope form
y – 5 = 0(x – 7)
y – 5 = 0 distributive property
y=5
0
m
 10
m=0
substitute slope in with
either point into point-slope form
{try to stay away from negatives}
Mr. Sims
Standard Form: Ax + By = C
Slope-Intercept Form: y = mx + b
Point-Slope Form: y – y1 = m(x – x1)
Find the slope and the y-intercept of the line described
by the given equation.
5. 3x – 5y = 10
-3x
-3x
-5y = -3x + 10
3
y  x2
5
3
slope =
5
get in slope-intercept form
divide both sides by -5
y-intercept = -2
Mr. Sims
Standard Form: Ax + By = C
Slope-Intercept Form: y = mx + b
Point-Slope Form: y – y1 = m(x – x1)
6. 5x – 3y – 15 = 0
+3y
+3y
3y = 5x - 15
5
y  x 5
3
5
slope =
3
y-intercept = -5
get in slope-intercept form
divide both sides by 3
7. 15 – 4(-2x – 3y) = 39
15 + 8x + 12y = 39
distributive property
-15 -8x
-15 – 8x
12y = -8x + 24
2
y x2
3
2
slope = 
3
divide by 12
y-intercept =
2
Mr. Sims
get in slope-intercept form
y = mx + b
-3x + 4y = -12
+3x
+3x
4y = 3x – 12
y  3x  3
4
divide by 4
slope = ¾
y-intercept = -3
Mr. Sims
A line has the given slope, y-intercept, or contains the indicated points.
Write an equation , in standard form, of each line.
1.) (-1,6) , (-4,2)
2.) (-1,5) , (-3,-4)
Algebra 2
Section 9.3 B
Assignment
3.) (5,-4) , (-2,-4)
4.) (0,7) , (4,0)
Find the slope and the y-intercept of the line described by the given equation.
5.) 2x + 3y = 9
6.) 7x + 3y = -21
7.) 5y – x + 20 = 0
8.) 7x – 3(4 – y) = 0
Mr. Sims
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Mr. Sims