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Write the equation of the line that passes through the points
(1,6) and
(-7,8). 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 $(1,6)$ and $(-7,8)$ . 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

(1,6)

and

(-7,8)

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

\newline

Answer:

Calculate slope: First, calculate the slope $m$ of the line using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ with the given points $(1,6)$ and $(-7,8)$ . $\newline$ $m = \frac{8 - 6}{-7 - 1}$ $\newline$ $m = \frac{2}{-8}$ $\newline$ $m = -\frac{1}{4}$
Write point-slope equation: Now that we have the slope, we can use one of the points and the slope to write the equation in point-slope form, which is $y - y_1 = m(x - x_1)$ . Let's use the point $(1,6)$ . $\newline$ $y - 6 = \left(-\frac{1}{4}\right)(x - 1)$
Final form: The equation $y - 6 = \left(-\frac{1}{4}\right)(x - 1)$ is already in point-slope form and does not need further simplification. It is not a vertical or horizontal line, so this is the final form.

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