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The x-intercept of a graph is the point where the graph crosses the x-axis. At this point, the value of y is always 0.

To find the x-intercept for a given equation, follow these steps:

• Set y to 0 in the equation
• Solve for x

Let's apply these steps to the equation \(-3x + 2y = 12\).

First, set y to 0:
\(-3x + 2(0) = 12\).

Now, simplify and solve for x:
\-3x = 12\
\ x = -4\

So, the x-intercept is \(-4, 0\).

The y-intercept of a graph is the point where the graph crosses the y-axis. At this point, the value of x is always 0.

To find the y-intercept for a given equation, follow these steps:

• Set x to 0 in the equation
• Solve for y

Let's apply these steps to the equation \(-3x + 2y = 12\).

First, set x to 0:
\(-3(0) + 2y = 12\).

Now, simplify and solve for y:
\2y = 12\
\ y = 6\

So, the y-intercept is \(0, 6\).

Solving linear equations involves finding the value of the variables that make the equation true. In a standard form linear equation \(Ax + By = C\), you can solve for one variable by isolating it on one side of the equation.

Here’s a step-by-step approach:

• Identify the variable you need to solve for
• Isolate the variable by performing the same operation on both sides of the equation
• Simplify the equation to solve for the variable

Using the equation \(-3x + 2y = 12\) as an example, we already solved for the intercepts by isolating x and y.

When solving for x (finding the x-intercept):
Set y to 0 and solve:
\ -3x = 12\
\ x = -4\

When solving for y (finding the y-intercept):
Set x to 0 and solve:
\ 2y = 12\
\ y = 6\

Understanding how to manipulate and simplify these equations is crucial for finding intercepts and solving various algebraic problems.