Questions: Determine the intercepts of the line. Do not round your answers. y-3=5(x-2) y-intercept: , ) x-intercept: ,

Determine the intercepts of the line. Do not round your answers. y-3=5(x-2) y-intercept: , ) x-intercept: ,
Transcript text: Determine the intercepts of the line. Do not round your answers. \[ y-3=5(x-2) \] $y$-intercept: $\square$ , $\square$ ) $x$-intercept: $\square$ , $\square$
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Solution

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Solution Steps

Step 1: Finding the \( y \)-intercept

To find the \( y \)-intercept, we set \( x = 0 \) in the equation \( y - 3 = 5(x - 2) \). Substituting \( x = 0 \):

\[ y - 3 = 5(0 - 2) \implies y - 3 = -10 \implies y = -7 \]

Thus, the \( y \)-intercept is:

\[ (0, -7) \]

Step 2: Finding the \( x \)-intercept

To find the \( x \)-intercept, we set \( y = 0 \) in the equation \( y - 3 = 5(x - 2) \). Substituting \( y = 0 \):

\[ 0 - 3 = 5(x - 2) \implies -3 = 5x - 10 \implies 5x = 7 \implies x = \frac{7}{5} \]

Thus, the \( x \)-intercept is:

\[ \left(\frac{7}{5}, 0\right) \]

Final Answer

The intercepts of the line are:

  • \( y \)-intercept: \(\boxed{(0, -7)}\)
  • \( x \)-intercept: \(\boxed{\left(\frac{7}{5}, 0\right)}\)
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