How do you find the intercepts for -3x-4y=18?

1 Answer
Nov 6, 2015

x=-6

y=-9/2

Explanation:

To find the x and y intercepts for an equation, you need to put the equation in Standard Form (y=mx+b).

Thus, we need to solve -3x -4y = 18 for y.

First, we can add 3x to both sides. Doing so yields:

=-4y=18+3x

or

=-4y=3x+18

Then, we need to divide both sides by -4 to isolate y.

y=(3x+18)/(-4)

Simplifying slightly gets you:

y=-(3x)/4-18/4

which equates to

y=-(3x)/4-9/2

Now that we have the equation in Standard form, we can look for the intercepts. Conceptually, an x-intercept will occur when y=0 and a y-intercept will occur when x=0.

So, simply plug in those values of 0 seperately to solve for each intercept.

Solving for the x-intercept:

(0)=-(3x)/4-9/2

Adding (3x)/4 to both sides results in:

(3x)/4=-9/2

Multiplying both sides by 4/3 gets:

x=(-9/2)(4/3)

or:

x=-6

Solving for the y-intercept:

y=-(3(0))/4-9/2

Canceling out the term with the 0 being multiplied to it gives:

y=-9/2

It is worthy to notice that the y-intercept of the equation, when put in Standard Form, is simply the term without the x in it (or the b term when written as y=mx+b).