Graph equations in slope-intercept form

An equation in slope-intercept form, $y=mx+b$ , represents a linear relationship in which $m$ is the constant rate of change in $y$ for each one-unit increase in $x$ , and $b$ is the $y$ -intercept $(0,b)$ . Graphing the equation involves plotting the intercept, using positive, negative, zero, or fractional slope to locate additional points, and interpreting the line as all ordered pairs that satisfy the equation; nonlinear graphs and vertical lines are outside this scope.

Detailed Explanation: Graph equations in slope-intercept form

An equation in slope-intercept form is

y=mx+b.

$m$ is the slope, or the change in $y$ for each 1-unit change in $x$ .
$b$ is the $y$ -intercept, the point where the line crosses the $y$ -axis: $(0,b)$ .

Example

Graph

y=-\frac{2}{3}x+4.

Step 1: Identify the slope and $y$ -intercept.

Compare the equation with $y=mx+b$ :

m=-\frac{2}{3}, \qquad b=4.

The $y$ -intercept is $(0,4)$ .

Step 2: Plot the $y$ -intercept.

Plot the point $(0,4)$ on the coordinate plane.

Step 3: Use the slope to find another point.

The slope is

-\frac{2}{3}=\frac{\text{rise}}{\text{run}}.

This means:

Move right 3 units.
Move down 2 units.

Starting at $(0,4)$ , this gives the point

(3,2).

Repeat the same movement to get another point:

(6,0).

Step 4: Draw the line.

Draw a straight line through the points $(0,4)$ , $(3,2)$ , and $(6,0)$ . Extend the line in both directions and add arrows.

The graph represents every ordered pair $(x,y)$ that makes the equation true. For example, when $x=3$ ,

y=-\frac{2}{3}(3)+4=-2+4=2,

so $(3,2)$ is on the line.

A negative slope means the line decreases as you move from left to right.

Learn by doing: Graph equations in slope-intercept form

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Slope - Find Equivalent - Slope Y Intercept Form to Graph

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