Question

y = 2/3x-4 Slope: X-intercept: y-intercept:

Answer 1

The Slope-Intercept form of the equation of a line is:

$y=mx+b$

Where "m" is the slope of the line and "b" is the y-intercept.

In this case you have the following equation written in Slope-Intercept form:

$y=\frac{2}{3}x-4$

Then, you can identify that:

$\begin{gathered} m=\frac{2}{3} \\ \\ b=-4 \end{gathered}$

By definition, the value of "y" is zero when the line intersects the x-axis:

$y=0$

Substitute this value into the equation given in the exercise and then solve for the variable "x", in order to find the x-intercept. This is:

$\begin{gathered} y=\frac{2}{3}x-4 \\ \\ 0=\frac{2}{3}x-4 \\ \\ 4=\frac{2}{3}x \\ \\ (3)(4)=2x \\ 12=2x \\ \\ \frac{12}{2}=x \\ \\ x=6 \end{gathered}$

Answers

Slope:

$m=\frac{2}{3}$

x-intercept:

$x=6$

y-intercept:

$b=-4$