IB AA · 4A Equations of Straight Lines
Solve a line for y, then read the gradient and the y-intercept.
Solve for y
Move the x term and the constant, then divide by the coefficient of y.
Read m and c
In y = mx + c, m is the gradient and c is the y-intercept.
Vertical line
If there is no y term, the line is x = a constant. It has no gradient.
Horizontal line
If there is no x term, the gradient is 0 and the equation is y = a constant.
The coefficient of y is 1 or −1.
2x − y − 8 = 0
−y = −2x + 8
Divide by −1.
y = 2x − 8
The gradient is 2.
The y-intercept is −8.
Answer: y = 2x − 8, gradient 2, y-intercept −8
2x − y + 6 = 0
−y = −2x − 6
Divide by −1.
y = 2x + 6
The gradient is 2.
The y-intercept is 6.
Answer: y = 2x + 6, gradient 2, y-intercept 6
3x − y − 9 = 0
y = 3x − 9
y = 3x − 9
The gradient is 3.
The y-intercept is −9.
Answer: y = 3x − 9, gradient 3, y-intercept −9
x + y − 4 = 0
y = −x + 4
y = −x + 4
The gradient is −1.
The y-intercept is 4.
Answer: y = −x + 4, gradient −1, y-intercept 4
4x − y − 8 = 0
−y = −4x + 8
Divide by −1.
y = 4x − 8
The gradient is 4.
The y-intercept is −8.
Answer: y = 4x − 8, gradient 4, y-intercept −8
2x − y = 0
y = 2x
y = 2x
The gradient is 2.
The y-intercept is 0.
Answer: y = 2x, gradient 2, y-intercept 0
Divide by the coefficient of y.
2x + y − 6 = 0
2y = −4x + 12
Divide by 2.
y = −2x + 6
The gradient is −2.
The y-intercept is 6.
Answer: y = −2x + 6, gradient −2, y-intercept 6
3x + 2y − 6 = 0
2y = −3x + 6
Divide by 2.
y = −32x + 3
The gradient is −32.
The y-intercept is 3.
Answer: y = −32x + 3, gradient −32, y-intercept 3
x − 2y + 4 = 0
−4y = −2x − 8
Divide by −4.
y = 12x + 2
The gradient is 12.
The y-intercept is 2.
Answer: y = 12x + 2, gradient 12, y-intercept 2
5x + 2y = 0
2y = −5x
Divide by 2.
y = −52x
The gradient is −52.
The y-intercept is 0.
Answer: y = −52x, gradient −52, y-intercept 0
x − 2y + 3 = 0
6y = 3x + 9
Divide by 6.
y = 12x + 32
The gradient is 12.
The y-intercept is 32.
Answer: y = 12x + 32, gradient 12, y-intercept 32
2x + y − 5 = 0
2y = −4x + 10
Divide by 2.
y = −2x + 5
The gradient is −2.
The y-intercept is 5.
Answer: y = −2x + 5, gradient −2, y-intercept 5
A vertical line, a horizontal line, and fractions.
3x + 6y − 4 = 0
6y = −3x + 4
Divide by 6.
y = −12x + 23
The gradient is −12.
The y-intercept is 23.
Answer: y = −12x + 23, gradient −12, y-intercept 23
x − 4 = 0
x = 4
The line is vertical, so it has no gradient and no y-intercept.
Answer: x = 4
y + 3 = 0
2y = 0 − 6
Divide by 2.
y = −3
The gradient is 0.
The y-intercept is −3.
Answer: y = −3, gradient 0, y-intercept −3
3x − 5y + 4 = 0
−5y = −3x − 4
Divide by −5.
y = 35x + 45
The gradient is 35.
The y-intercept is 45.
Answer: y = 35x + 45, gradient 35, y-intercept 45
6x + 4y − 3 = 0
4y = −6x + 3
Divide by 4.
y = −32x + 34
The gradient is −32.
The y-intercept is 34.
Answer: y = −32x + 34, gradient −32, y-intercept 34
2x + 3y − 7 = 0
−3y = 2x − 7
Divide by −3.
y = −23x + 73
The gradient is −23.
The y-intercept is 73.
Answer: y = −23x + 73, gradient −23, y-intercept 73
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