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A line passes through the points $(-1,-9)$ and $(1,7)$ . 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,-9)

and

(1,7)

. 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 $m$ using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ with points $(-1, -9)$ and $(1, 7)$ . $\newline$ Calculation: $m = \frac{7 - (-9)}{1 - (-1)} = \frac{16}{2} = 8$ .
Find Y-Intercept: Step $2$ : Use the slope $m = 8$ and one of the points, say $(-1, -9)$ , to find the y-intercept $b$ using the formula $y = mx + b$ . $\newline$ Calculation: $-9 = 8(-1) + b$ , $-9 = -8 + b$ , $b = -9 + 8$ , $b = -1$ .
Write Equation: Step $3$ : Write the equation of the line in slope-intercept form $y = mx + b$ using $m = 8$ and $b = -1$ . $\newline$ Calculation: $y = 8x - 1$ .

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