H Algebra 2/Trig · Unit 1
Rewrite Ax + By + C = 0 as y = mx + c. Read the slope, y-intercept, zero, and parallel or perpendicular slopes.
Solve for y
The form y = mx + c shows the slope m and the y-intercept c at once. Isolate y.
Y-intercept
The y-intercept is (0, c). It is where the line crosses the y-axis.
Zero of the line
A zero is an x-intercept: set y = 0 and solve for x. Write it as a point (x, 0).
Parallel and perpendicular
Parallel lines have the same slope. Perpendicular slopes are negative reciprocals: m⊥ = −1m.
Write y = mx + c. Name the y-intercept, the zero, and the slope.
The formula is
y = mx + c
Solve for y.
2x + 4y − 8 = 0
4y = −2x + 8
Divide both sides by 4.
y = −12x + 2
b. Y-intercept: x = 0.
(0, 2)
c. Zero: set y = 0.
0 = −12x + 2
−12x = −2
x = 4
(4, 0)
d. Slope.
−12
Answer: a. y = −12x + 2b. (0, 2)c. (4, 0)d. −12
The formula is
y = mx + c
Solve for y.
3x + 3y − 9 = 0
3y = −3x + 9
Divide both sides by 3.
y = −x + 3
b. Y-intercept: x = 0.
(0, 3)
c. Zero: set y = 0.
0 = −x + 3
−1x = −3
x = 3
(3, 0)
d. Slope.
−1
Answer: a. y = −x + 3b. (0, 3)c. (3, 0)d. −1
The formula is
y = mx + c
Solve for y.
4x + 2y − 10 = 0
2y = −4x + 10
Divide both sides by 2.
y = −2x + 5
b. Y-intercept: x = 0.
(0, 5)
c. Zero: set y = 0.
0 = −2x + 5
−2x = −5
x = 52
(52, 0)
d. Slope.
−2
Answer: a. y = −2x + 5b. (0, 5)c. (52, 0)d. −2
The formula is
y = mx + c
Solve for y.
6x + 3y + 12 = 0
3y = −6x − 12
Divide both sides by 3.
y = −2x − 4
b. Y-intercept: x = 0.
(0, −4)
c. Zero: set y = 0.
0 = −2x − 4
−2x = 4
x = −2
(−2, 0)
d. Slope.
−2
Answer: a. y = −2x − 4b. (0, −4)c. (−2, 0)d. −2
The formula is
y = mx + c
Solve for y.
2x − 4y + 8 = 0
−4y = −2x − 8
Divide both sides by −4.
y = 12x + 2
b. Y-intercept: x = 0.
(0, 2)
c. Zero: set y = 0.
0 = 12x + 2
12x = −2
x = −4
(−4, 0)
d. Slope.
12
Answer: a. y = 12x + 2b. (0, 2)c. (−4, 0)d. 12
The formula is
y = mx + c
Solve for y.
5x + 5y − 15 = 0
5y = −5x + 15
Divide both sides by 5.
y = −x + 3
b. Y-intercept: x = 0.
(0, 3)
c. Zero: set y = 0.
0 = −x + 3
−1x = −3
x = 3
(3, 0)
d. Slope.
−1
Answer: a. y = −x + 3b. (0, 3)c. (3, 0)d. −1
Also find the zero.
The formula is
y = mx + c
Solve for y.
4x + 2y − 12 = 0
2y = −4x + 12
Divide both sides by 2.
y = −2x + 6
b. Y-intercept: x = 0.
(0, 6)
c. Zero: set y = 0.
0 = −2x + 6
−2x = −6
x = 3
(3, 0)
d. Slope.
−2
Answer: a. y = −2x + 6b. (0, 6)c. (3, 0)d. −2
The formula is
y = mx + c
Solve for y.
6x + 2y − 8 = 0
2y = −6x + 8
Divide both sides by 2.
y = −3x + 4
b. Y-intercept: x = 0.
(0, 4)
c. Zero: set y = 0.
0 = −3x + 4
−3x = −4
x = 43
(43, 0)
d. Slope.
−3
Answer: a. y = −3x + 4b. (0, 4)c. (43, 0)d. −3
The formula is
y = mx + c
Solve for y.
3x − 6y + 18 = 0
−6y = −3x − 18
Divide both sides by −6.
y = 12x + 3
b. Y-intercept: x = 0.
(0, 3)
c. Zero: set y = 0.
0 = 12x + 3
12x = −3
x = −6
(−6, 0)
d. Slope.
12
Answer: a. y = 12x + 3b. (0, 3)c. (−6, 0)d. 12
The formula is
y = mx + c
Solve for y.
8x + 4y + 16 = 0
4y = −8x − 16
Divide both sides by 4.
y = −2x − 4
b. Y-intercept: x = 0.
(0, −4)
c. Zero: set y = 0.
0 = −2x − 4
−2x = 4
x = −2
(−2, 0)
d. Slope.
−2
Answer: a. y = −2x − 4b. (0, −4)c. (−2, 0)d. −2
The formula is
y = mx + c
Solve for y.
10x + 5y − 20 = 0
5y = −10x + 20
Divide both sides by 5.
y = −2x + 4
b. Y-intercept: x = 0.
(0, 4)
c. Zero: set y = 0.
0 = −2x + 4
−2x = −4
x = 2
(2, 0)
d. Slope.
−2
Answer: a. y = −2x + 4b. (0, 4)c. (2, 0)d. −2
The formula is
y = mx + c
Solve for y.
2x + 6y − 12 = 0
6y = −2x + 12
Divide both sides by 6.
y = −13x + 2
b. Y-intercept: x = 0.
(0, 2)
c. Zero: set y = 0.
0 = −13x + 2
−13x = −2
x = 6
(6, 0)
d. Slope.
−13
Answer: a. y = −13x + 2b. (0, 2)c. (6, 0)d. −13
Full list: form, intercept, zero, slope, parallel, perpendicular.
The formula is
y = mx + c
Solve for y.
6x + 4y − 12 = 0
4y = −6x + 12
Divide both sides by 4.
y = −32x + 3
b. Y-intercept: x = 0.
(0, 3)
c. Zero: set y = 0.
0 = −32x + 3
−32x = −3
x = 2
(2, 0)
d. Slope.
−32
e. Parallel lines have the same slope.
−32
f. Perpendicular slopes are negative reciprocals.
The formula is
m⊥ = −1m
23
Answer: a. y = −32x + 3b. (0, 3)c. (2, 0)d. −32e. −32f. 23
The formula is
y = mx + c
Solve for y.
8x + 12y − 24 = 0
12y = −8x + 24
Divide both sides by 12.
y = −23x + 2
b. Y-intercept: x = 0.
(0, 2)
c. Zero: set y = 0.
0 = −23x + 2
−23x = −2
x = 3
(3, 0)
d. Slope.
−23
e. Parallel lines have the same slope.
−23
f. Perpendicular slopes are negative reciprocals.
The formula is
m⊥ = −1m
32
Answer: a. y = −23x + 2b. (0, 2)c. (3, 0)d. −23e. −23f. 32
The formula is
y = mx + c
Solve for y.
9x + 6y + 18 = 0
6y = −9x − 18
Divide both sides by 6.
y = −32x − 3
b. Y-intercept: x = 0.
(0, −3)
c. Zero: set y = 0.
0 = −32x − 3
−32x = 3
x = −2
(−2, 0)
d. Slope.
−32
e. Parallel lines have the same slope.
−32
f. Perpendicular slopes are negative reciprocals.
The formula is
m⊥ = −1m
23
Answer: a. y = −32x − 3b. (0, −3)c. (−2, 0)d. −32e. −32f. 23
The formula is
y = mx + c
Solve for y.
5x − 10y + 15 = 0
−10y = −5x − 15
Divide both sides by −10.
y = 12x + 32
b. Y-intercept: x = 0.
(0, 32)
c. Zero: set y = 0.
0 = 12x + 32
12x = −32
x = −3
(−3, 0)
d. Slope.
12
e. Parallel lines have the same slope.
12
f. Perpendicular slopes are negative reciprocals.
The formula is
m⊥ = −1m
−2
Answer: a. y = 12x + 32b. (0, 32)c. (−3, 0)d. 12e. 12f. −2
The formula is
y = mx + c
Solve for y.
4x + 8y − 20 = 0
8y = −4x + 20
Divide both sides by 8.
y = −12x + 52
b. Y-intercept: x = 0.
(0, 52)
c. Zero: set y = 0.
0 = −12x + 52
−12x = −52
x = 5
(5, 0)
d. Slope.
−12
e. Parallel lines have the same slope.
−12
f. Perpendicular slopes are negative reciprocals.
The formula is
m⊥ = −1m
2
Answer: a. y = −12x + 52b. (0, 52)c. (5, 0)d. −12e. −12f. 2
The formula is
y = mx + c
Solve for y.
3x + 12y − 18 = 0
12y = −3x + 18
Divide both sides by 12.
y = −14x + 32
b. Y-intercept: x = 0.
(0, 32)
c. Zero: set y = 0.
0 = −14x + 32
−14x = −32
x = 6
(6, 0)
d. Slope.
−14
e. Parallel lines have the same slope.
−14
f. Perpendicular slopes are negative reciprocals.
The formula is
m⊥ = −1m
4
Answer: a. y = −14x + 32b. (0, 32)c. (6, 0)d. −14e. −14f. 4
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