Write an equation from a linear graph

A linear graph represents a constant rate of change: the slope gives the change in $y$ for each unit change in $x$ , and the $y$ -intercept gives the value of $y$ when $x=0$ . The relationship can be expressed in $y=mx+b$ form by reading or calculating these features from a coordinate grid, including positive, negative, zero, and simple fractional slopes; vertical lines and more general equation forms are outside this scope.

Detailed Explanation: Write an equation from a linear graph

A linear equation can be written in the form

y=mx+b

where:

$m$ is the slope, or the change in $y$ for each change in $x$ .
$b$ is the $y$ -intercept, where the line crosses the $y$ -axis.

Example: A graph crosses the $y$ -axis at $(0,-1)$ and also passes through $(2,3)$ . Write an equation for the line.

Find the $y$ -intercept.
The graph crosses the $y$ -axis at $-1$ , so

b=-1.

Find the slope.
Use the two points $(0,-1)$ and $(2,3)$ :

m=\frac{\text{change in }y}{\text{change in }x} =\frac{3-(-1)}{2-0} =\frac{4}{2}=2.

Substitute $m$ and $b$ into $y=mx+b$ .

y=2x-1

So, the equation of the line is

\boxed{y=2x-1}.

You can check the equation using the points. When $x=0$ , $y=2(0)-1=-1$ , and when $x=2$ , $y=2(2)-1=3$ , matching the graph.

Learn by doing: Write an equation from a linear graph

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Slope of a Line - Select Linear Equation Based on Graph

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Write an equation from a linear graph

Detailed Explanation: Write an equation from a linear graph

Learn by doing: Write an equation from a linear graph

Practice with unlimited practice problems

Practice:

Slope of a Line - Select Linear Equation Based on Graph