Questions: Find the x-intercept and y-intercept of the line. 7x-4y=28 x-intercept: y-intercept:

Find the x-intercept and y-intercept of the line. 7x-4y=28 x-intercept: y-intercept:
Transcript text: Find the $x$-intercept and $y$-intercept of the line. \[ 7 x-4 y=28 \] x -intercept: $\square$ y -intercept: $\square$
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Solution

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Solution Steps

To find the intercepts of the line given by the equation \(7x - 4y = 28\):

  1. x-intercept: Set \(y = 0\) in the equation and solve for \(x\).
  2. y-intercept: Set \(x = 0\) in the equation and solve for \(y\).
Step 1: Find the \(x\)-intercept

To find the \(x\)-intercept, we set \(y = 0\) in the equation \(7x - 4y = 28\):

\[ 7x - 4(0) = 28 \implies 7x = 28 \implies x = \frac{28}{7} = 4 \]

Thus, the \(x\)-intercept is \(4\).

Step 2: Find the \(y\)-intercept

To find the \(y\)-intercept, we set \(x = 0\) in the equation \(7x - 4y = 28\):

\[ 7(0) - 4y = 28 \implies -4y = 28 \implies y = \frac{28}{-4} = -7 \]

Thus, the \(y\)-intercept is \(-7\).

Final Answer

The \(x\)-intercept is \(\boxed{4}\) and the \(y\)-intercept is \(\boxed{-7}\).

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