Question

Given the following equation, find the following: 3x – 2y = 12A. x-interceptB. y-interceptC. Slope

Answer 1

We are given the following equation

`3x-2y=12`

A. x-intercept

The x-intercept is the point where the line intersects the x-axis.

It can be found by substituting y = 0 into the equation.

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

Therefore, the x-intercept is 4

x-intercept = (4, 0)

B. y-intercept

The y-intercept is the point where the line intersects the y-axis.

It can be found by substituting x = 0 into the equation.

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

Therefore, the y-intercept is -6

y-intercept = (0, -6)

C. Slope

Recall that the slope-intercept form of an equation is given by

`y=mx+b`

Where m is the slope and b is the y-intercept.

Let us convert the given equation into the above slope-intercept form.

`\begin{gathered} 3x-2y=12 \\ -2y=-3x+12 \\ y=(-3x+12)/(-2) \\ y=(-3x)/(-2)+(12)/(-2) \\ y=(3)/(2)x-6 \end{gathered}`

Comparing the above equation with the slope-intercept form, we see that the slope is 3/2

Slope = 3/2