how would I find the x-intercept and y-intercept of 2x-3y=24?

To find the y intercept, ask yourself this: if you set x = 0 into the equation 2x-3y=24, what is the corresponding value of y? And to find the x intercept, it's a similar process: set y=0, and determine x.

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Originally Posted by dee77

how would i find the x-intercept and y-intercept of 2x-3y=24?

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To find the x intercepts of an equation, let y = 0 and to find the y-intercepts, let x = 0.

What is an intercept anyway?

An intercept is a point in the form (x, y) on either the x- or y-axis through which a graph passes. In other words, it is a point through which a graph (picture of an equation or function) will travel through on the xy-plane.

We have 2x - 3y = 24... By the way, this is called a linear equation.

Let's find the x-intercepts, if any, first but of course, you could find the y-intercepts, if any, as your first step.

To find the x-intercepts, we let y = 0 in the equation and then simplify.

2x - 3(0) = 24

2x - 0 = 24

2x = 24

x = 24/2

x = 12

Our x-intercept is the point (12, 0).

Let's now find the y-intercept.

We let x = 0 and simplify.

2(0) - 3y = 24

0 - 3y = 24

-3y = 24

y = 24/-3

y = -8

Our y-intercept is the point (0, -8)

What does this mean? It means that when you graph your equation 2x - 3y = 24 on the xy-plane, the picture of the equation (called a graph), will go through the two points we found.

Is this clear?