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A line passes through the points $(-1,-8)$ and $(1,6)$ . Write its equation in slope-intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest form.

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Write a linear equation from two points

Full solution

Q. A line passes through the points

(-1,-8)

and

(1,6)

. Write its equation in slope-intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest form.

Calculate slope: Step $1$ : Calculate the slope of the line using the points $(-1, -8)$ and $(1, 6)$ . $\newline$ Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ $\newline$ $m = \frac{6 - (-8)}{1 - (-1)}$ $\newline$ $m = \frac{14}{2}$ $\newline$ $m = 7$
Find y-intercept: Step $2$ : Use the slope and one point to find the y-intercept, $b$ . Using point $(1, 6)$ and slope $m = 7$ in the equation $y = mx + b$ . $6 = 7(1) + b$ $6 = 7 + b$ $b = 6 - 7$ $b = -1$
Write equation: Step $3$ : Write the equation of the line in slope-intercept form. $\newline$ Using $m = 7$ and $b = -1$ , the equation is: $\newline$ $y = 7x - 1$

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