What are the intercepts of the line y=9/2x - 4?

May 9, 2018

The y-intercept for the given line is $\left(0 , - 4\right)$.

The x-intercept is $\left(\frac{8}{9} , 0\right)$ or $\left(0.889 , 0\right)$.

Explanation:

Find the intercepts:

$y = \frac{9}{2} x - 4$

This is a linear equation in slope-intercept form:

$y = m x + b$,

where:

$m$ is the slope $\left(\frac{9}{2}\right)$ and $b$ is the y-intercept $\left(- 4\right)$.

Y-intercept: value of $y$ when $x = 0$.

By definition, the y-intercept for the given line is $\left(0 , - 4\right)$.

X-intercept: value of $x$ when $y = 0$.

Substitute $0$ for $y$ and solve for $x$.

$0 = \frac{9}{2} x - 4$

Add $4$ to both sides.

$4 = \frac{9}{2} x$

Multiply both sides by $2$.

$8 = 9 x$

Divide both sides by $9$.

$\frac{8}{9} = x$

The x-intercept is $\left(\frac{8}{9} , 0\right)$ or $\left(0.889 , 0\right)$.

You can graph the given line by plotting the x- and y-intercepts and drawing a straight line through them.

graph{y=9/2x-4 [-9.77, 10.23, -7.61, 2.39]}