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

$\frac{2x}{2}=\frac{-12}{2}\rightarrow x=-6$

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

$\frac{-3y}{-3}=\frac{-12}{-3}$

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.