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# Graphing Using x- and y- Intercepts

Once we know both the x-intercept and the y-intercept, we can graph the equation.

Example 1

Graph 3x + 5y = 15 using the x- and y- intercept.

Solution

First, find the intercepts.

 To find the y -intercept, let x = 0. To find the x-intercept, let y = 0. 3 Â· 0 + 5y = 15 3x + 5 Â· 0 = 15 5y = 15 3x = 15 y = 3 x = 5 The y-intercept is 3. The x-intercept is 5. The ordered pair is (0, 3). The ordered pair is ( 5, 0)

We now graph these two points and draw the line that contains them.

## Slope-Intercept Form

The slope-intercept form is a special case of the point-slope form, where the given point of the line (x 0 , y 0 ) lies on the y-axis, so x 0 = 0. This means that the equation is of the form y - y 0 = mx, or y = mx + y 0 . So, the equation is given explicitly when we know both the intercept and the slope and it is simpler than the more general point-slope form. This is the most common form for the equation of a line.

Key Idea An equation for a line is said to be in slope-intercept form when it is of the form y = mx + b, where m is the slope of the line and b is the y-coordinate of the y-intercept. Any line that is not vertical has an equation that can be written in slope-intercept form.

The equation of a vertical line cannot be written in slope-intercept form because the slope of a vertical line is undefined; that is, it has no slope.

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