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=(2)/(3)x-4`

Then, you can identify that:

`\begin{gathered} m=(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=(2)/(3)x-4 \\ \\ 0=(2)/(3)x-4 \\ \\ 4=(2)/(3)x \\ \\ (3)(4)=2x \\ 12=2x \\ \\ (12)/(2)=x \\ \\ x=6 \end{gathered}`

Answers

Slope:

`m=(2)/(3)`

x-intercept:

`x=6`

y-intercept:

`b=-4`