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Write the equation of the line that passes through the points
(-5,9) and
(0,-7). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
Answer:

Write the equation of the line that passes through the points $(-5,9)$ and $(0,-7)$ . Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line. $\newline$ Answer:

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Write a linear equation from two points

Full solution

Q. Write the equation of the line that passes through the points

(-5,9)

and

(0,-7)

. Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

\newline

Answer:

Calculate the slope: Calculate the slope $m$ of the line using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ with the given points $(-5,9)$ and $(0,-7)$ . $\newline$ $m = \frac{-7 - 9}{0 - (-5)}$ $\newline$ $m = \frac{-16}{5}$ $\newline$ The slope of the line is $-\frac{16}{5}$ .
Choose a point: Choose one of the points to use in the point-slope form equation. We will use the point $(-5,9)$ . $\newline$ The point-slope form of the equation of a line is $y - y_1 = m(x - x_1)$ , where $m$ is the slope and $(x_1, y_1)$ is a point on the line. $\newline$ Substitute the slope and the point into the equation: $\newline$ $y - 9 = \frac{-16}{5}(x - (-5))$ $\newline$ $y - 9 = \frac{-16}{5}(x + 5)$
Substitute slope and point: Simplify the equation by distributing the slope on the right side: $\newline$ $y - 9 = \left(-\frac{16}{5}\right)x - \left(\frac{16}{5}\right)(5)$ $\newline$ $y - 9 = \left(-\frac{16}{5}\right)x - 16$
Simplify the equation: The equation is now in point-slope form, but we can check if it can be simplified further. Since there are no like terms to combine on the right side, the equation is already fully simplified.

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