Question

Ex 5) Find the x-intercept and y-intercept of the graph 2x - 3y = -12. Thengraph the equation

Answer 1

The given equation is

`2x-3y=-12`

This is a linear equation, which must have a y-intercept and x-intercept.

To find x-intercept we just need to replace y=0 in the equation

`2x-3(0)=-12`

Then, we solve for x

`2x-0=-12\rightarrow2x=-12`

Finally, we divide by 2

`(2x)/(2)=(-12)/(2)\rightarrow x=-6`

This means the x-intercept is at (-6,0).

On the other hand, to find y-intercept we need to replace x=0 in the equation

`2(0)-3y=-12`

Then, we solve for y

`-3y=-12`

At last, we divide by -3

`(-3y)/(-3)=(-12)/(-3)`

So,

`y=4`

Therefore, the y-intercept is at (0,4).

To graph the function, we just need to graph each axis intercept and draw the line.