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Converting a Linear Equation from General to SlopeIntercept Form
(KS4, Year 10)
The Lesson
A linear equation is an equation that represents a line. We can convert a linear equation from general form to slopeintercept form.Why Convert from General Form to SlopeIntercept Form?
The same line can be written in general form and slopeintercept form. The two forms of linear equation tell us different things about the line.
In general form, a, b and c do not tell us anything about the line.

In slopeintercept form,
• m tells us the slope of a line
• c tells us the yintercept of a line.
How to Convert a Linear Equation from General to SlopeIntercept Form
Using algebra, we can take the general form of a linear equation and make it look like the slope intercept form.
Start with the linear equation in general form:

Subtract ax from both sides. This has the effect of moving the ax to the other side of the equals sign (=) and changing its sign from positive to negative:

Subtract c from both sides:

Divide both sides by b:
 The slope is given by −^{a}⁄_{b}.
 The yintercept is given by −^{c}⁄_{b}.
A Real Example of How to Convert a Linear Equation from General to SlopeIntercept Form
Convert the linear equation in general form below to slopeintercept form.Question
Find the yintercept of the line given by the linear equation shown below.StepbyStep:
1
Subtract 4x from both sides:
4x + 2y + 6 − 4x = 0 − 4x
2y + 6 = −4x
2
Subtract 6 from both sides:
2y + 6 − 6 = − 4x − 6
2y = −4x − 6
3
Divide both sides by 2:
2y ÷ 2 = (− 4x − 6) ÷ 2
y = −2x − 3
Answer:
We have converted 4x + 2y + 6 (in general form) to y = −2x − 3 (in slopeintercept form).Interactive Widget
You can use this interactive widget to create a graph of a linear equation in slope intercept form. Use the buttons to change the values of the linear equation. Do you disagree with something on this page?
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