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The x-intercept is the point where a graph crosses the x-axis. To find this point, we need to set y to 0 in the given equation and solve for x. This is because at the x-intercept, the value of y is always zero. Let's see how this works with an example.

Consider the equation: 3x - 5y = 30

First, set y = 0:

3x - 5(0) = 30

Simplify:

3x = 30

Finally, divide both sides by 3:

x = 10

This means the x-intercept is at (10, 0). By following these steps, you can easily find the x-intercept for any linear equation.

The y-intercept is where the graph crosses the y-axis. At this intercept, the value of x is always zero. To find the y-intercept, we substitute x = 0 into the equation and solve for y.

Here’s how to find the y-intercept for the equation: 3x - 5y = 30

Start by setting x to 0:

3(0) - 5y = 30

Simplify the equation:

-5y = 30

Then, divide both sides by -5:

y = -6

Therefore, the y-intercept is (0, -6). Using these steps, you can determine the y-intercept for any linear equation.

A linear equation is an equation between two variables that, when plotted on a graph, forms a straight line. Linear equations follow the standard form: Ax + By = C

Here, A, B, and C are constants. The intercepts provide key points that help us draw the graph of these equations.

To understand the concept better, think of linear equations as instructions for drawing straight lines on a plane. By finding the x-intercept and y-intercept, you can easily plot the points and draw the line.

Linear equations are fundamental in algebra because they model relationships where one variable depends linearly on another. Mastering intercepts helps in graphing these relationships quickly. By breaking down intercept calculations into simple steps, we can make sense of these important concepts with ease.