Questions: Find the y-intercept and x-intercept of the line. 3 x-7 y=-10 y-intercept: x-intercept:

Find the y-intercept and x-intercept of the line. 3 x-7 y=-10 y-intercept: x-intercept:
Transcript text: Find the $y$-intercept and $x$-intercept of the line. \[ 3 x-7 y=-10 \] $y$-intercept: $\square$ $x$-intercept: $\square$
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Solution

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Solution Steps

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

To find the \( y \)-intercept, we set \( x = 0 \) in the equation \( 3x - 7y = -10 \).

\[ 3(0) - 7y = -10 \implies -7y = -10 \implies y = \frac{-10}{-7} \implies y = \frac{10}{7} \]

So, the \( y \)-intercept is \( \left(0, \frac{10}{7}\right) \).

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

To find the \( x \)-intercept, we set \( y = 0 \) in the equation \( 3x - 7y = -10 \).

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

So, the \( x \)-intercept is \( \left(\frac{-10}{3}, 0\right) \).

Final Answer

\( y \)-intercept: \(\boxed{\left(0, \frac{10}{7}\right)}\)

\( x \)-intercept: \(\boxed{\left(\frac{-10}{3}, 0\right)}\)

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