Question

How do you find the x and y intercept of `3y = 2x + 24`?

Answer 1

`x` intercept = -12, #y intercept = +8

Explanation:

The `x` intercept of a straight line refers to the (signed) distance from the origin of the point where the line intersects the `x` axis.

Now, all points on the given line must satisfy the equation

`3y=2x+24`

On the other hand, any point on the `x` axis must satisfy `y=0`. Thus, to obtain the `x` intercept of a straight line we must substitute `y=0` in its equation.

This gives

`2x+24=0`

and thus `x=-12`.

Similarly, substituting `x=0` gives the `y` intercept as +8.

Alternatively, we could have expressed the equation of the straight line in the form `x/a+y/b=1` and directly read off the values of `a` and `b` as the `x` and `y` intercepts, respectively.

In this case, rearranging and dividing both sides by 24 gives

`3y-2x =24 implies {3y-2x}/24=1 implies y/8 - x/12=1`

or

`x/{-12} +y/8=1`