Converting a Linear Equation from General to Slope-Intercept Form
(KS4, Year 10)
The LessonA linear equation is an equation that represents a line. We can convert a linear equation from general form to slope-intercept form.
Why Convert from General Form to Slope-Intercept Form?The same line can be written in general form and slope-intercept 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 slope-intercept form,
• m tells us the slope of a line
• c tells us the y-intercept of a line.
How to Convert a Linear Equation from General to Slope-Intercept FormUsing 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 y-intercept is given by −c⁄b.
A Real Example of How to Convert a Linear Equation from General to Slope-Intercept FormConvert the linear equation in general form below to slope-intercept form.
QuestionFind the y-intercept of the line given by the linear equation shown below.
Subtract 4x from both sides:
4x + 2y + 6 − 4x = 0 − 4x
2y + 6 = −4x
Subtract 6 from both sides:
2y + 6 − 6 = − 4x − 6
2y = −4x − 6
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 slope-intercept form).
Interactive WidgetYou 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.
Lesson SlidesThe slider below gives a real example of how to convert a linear equation from general form to slope-intercept form. Open the slider in a new tab
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