IB AA · 4A Equations of Straight Lines
Find where a line meets the axes.
x-intercept
Set y = 0, then solve for x. The point is (a, 0).
y-intercept
Set x = 0, then solve for y. The point is (0, b).
From y = mx + c
The y-intercept is c. The x-intercept is the x that makes y = 0.
Missing intercept
A horizontal line has no x-intercept, unless it is the x-axis. A vertical line has no y-intercept.
Both intercepts are integers.
3x + 2y − 12 = 0
On the x-axis, y = 0.
3x = 12
x = 123
x = 4
On the y-axis, x = 0.
2y = 12
y = 122
y = 6
Answer: x-intercept (4, 0), y-intercept (0, 6)
x − y − 3 = 0
On the x-axis, y = 0.
x = 3
x = 3
On the y-axis, x = 0.
−y = 3
y = −3
Answer: x-intercept (3, 0), y-intercept (0, −3)
2x + y − 8 = 0
On the x-axis, y = 0.
2x = 8
x = 82
x = 4
On the y-axis, x = 0.
y = 8
y = 8
Answer: x-intercept (4, 0), y-intercept (0, 8)
x + 2y − 6 = 0
On the x-axis, y = 0.
x = 6
x = 6
On the y-axis, x = 0.
2y = 6
y = 62
y = 3
Answer: x-intercept (6, 0), y-intercept (0, 3)
3x − y + 3 = 0
On the x-axis, y = 0.
3x = −3
x = −33
x = −1
On the y-axis, x = 0.
−y = −3
y = 3
Answer: x-intercept (−1, 0), y-intercept (0, 3)
2x + y − 4 = 0
On the x-axis, y = 0.
4x = 8
x = 84
x = 2
On the y-axis, x = 0.
2y = 8
y = 82
y = 4
Answer: x-intercept (2, 0), y-intercept (0, 4)
Clear a coefficient that is not 1.
2x + 3y − 18 = 0
On the x-axis, y = 0.
2x = 18
x = 182
x = 9
On the y-axis, x = 0.
3y = 18
y = 183
y = 6
Answer: x-intercept (9, 0), y-intercept (0, 6)
2x − 3y − 6 = 0
On the x-axis, y = 0.
2x = 6
x = 62
x = 3
On the y-axis, x = 0.
−3y = 6
y = 6−3
y = −2
Answer: x-intercept (3, 0), y-intercept (0, −2)
3x + 4y − 12 = 0
On the x-axis, y = 0.
3x = 12
x = 123
x = 4
On the y-axis, x = 0.
4y = 12
y = 124
y = 3
Answer: x-intercept (4, 0), y-intercept (0, 3)
5x − 2y + 10 = 0
On the x-axis, y = 0.
5x = −10
x = −105
x = −2
On the y-axis, x = 0.
−2y = −10
y = −10−2
y = 5
Answer: x-intercept (−2, 0), y-intercept (0, 5)
2x + 5y − 10 = 0
On the x-axis, y = 0.
2x = 10
x = 102
x = 5
On the y-axis, x = 0.
5y = 10
y = 105
y = 2
Answer: x-intercept (5, 0), y-intercept (0, 2)
2x − y + 3 = 0
On the x-axis, y = 0.
6x = −9
x = −96
x = −32
On the y-axis, x = 0.
−3y = −9
y = −9−3
y = 3
Answer: x-intercept (−32, 0), y-intercept (0, 3)
Horizontal, vertical, and a line through the origin.
5x − 2y − 20 = 0
On the x-axis, y = 0.
5x = 20
x = 205
x = 4
On the y-axis, x = 0.
−2y = 20
y = 20−2
y = −10
Answer: x-intercept (4, 0), y-intercept (0, −10)
x − 5 = 0
On the x-axis, y = 0.
2x = 10
x = 102
x = 5
There is no y-intercept. The line is vertical.
Answer: x-intercept (5, 0)
y + 3 = 0
There is no x-intercept. The line is horizontal.
On the y-axis, x = 0.
3y = −9
y = −93
y = −3
Answer: y-intercept (0, −3)
2x − 3y + 6 = 0
On the x-axis, y = 0.
4x = −12
x = −124
x = −3
On the y-axis, x = 0.
−6y = −12
y = −12−6
y = 2
Answer: x-intercept (−3, 0), y-intercept (0, 2)
3x + 5y − 7 = 0
On the x-axis, y = 0.
3x = 7
x = 73
On the y-axis, x = 0.
5y = 7
y = 75
Answer: x-intercept (73, 0), y-intercept (0, 75)
x − 2y = 0
On the x-axis, y = 0.
2x = 0
x = 0
On the y-axis, x = 0.
−4y = 0
y = 0−4
y = 0
Answer: x-intercept (0, 0), y-intercept (0, 0)
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