Question

Given 3×-2y=12,state the x and y intercepts and the slope.Then graph the equation

Answer 1

Given:

The equation of the line is :

`3x-2y=12`

The x- intercepts are the points where the y-coordinate is zero.

Hence,

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

Thus, the x- intercept is (4,0)

The y-intercept is the point where x-coordinate is zero,hence

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

Hence, the y-intercept is (0,- 6)

Now, the slope is given by 'm' in the standard equation of line: y = mx + c

Comparing given equation with this standard form,

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

Hence, the slope is 3/2.

To graph the equation,plot the points (4,0) and (0,- 6 )

This is the graph of the line.