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The x-intercept of a linear equation is the point where the graph of the equation crosses the x-axis. To find this point, you need to set the value of y to 0 and solve for x.
In the equation [ -2x + 4y = 12 ], set y to 0:[ -2x + 4(0) = 12 ]Now simplify:[ -2x = 12 ]Next, solve for x by dividing both sides of the equation by -2:[ x = -6 ]Therefore, the x-intercept is (-6, 0). This means that the graph crosses the x-axis at the point (-6, 0). Remember, at the x-intercept, y will always be 0.

The y-intercept of a linear equation is the point where the graph crosses the y-axis. To find this point, you need to set the value of x to 0 and solve for y.
Given the equation [ -2x + 4y = 12 ], set x to 0:[ -2(0) + 4y = 12 ]Now simplify:[ 4y = 12 ]Then solve for y by dividing both sides by 4:[ y = 3 ]So, the y-intercept is (0, 3). This indicates that the graph intersects the y-axis at (0, 3). Note that at the y-intercept, x will always be 0.

Solving linear equations often involves finding the x- and y-intercepts. A linear equation in two variables typically looks like this: [ ax + by = c ]
Here's a step-by-step method for solving:

1. Find the x-intercept: Set y to 0, then solve for x.
2. Find the y-intercept: Set x to 0, then solve for y.

Let's use our example again: [ -2x + 4y = 12 ]To find the x-intercept:
1. Set y to 0: [ -2x + 4(0) = 12 ]2. Simplify: [ -2x = 12 ]3. Solve for x by dividing by -2: [ x = -6 ]Thus, the x-intercept is (-6, 0).
To find the y-intercept:
1. Set x to 0: [ -2(0) + 4y = 12 ]2. Simplify: [ 4y = 12 ]3. Divide by 4 to solve for y: [ y = 3 ]So, the y-intercept is (0, 3).
By following these steps, you can easily find the points where the graph intersects the x- and y-axes, which helps in graphing the equation and understanding its behavior.