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A line passes through the points $(-2,-3)$ and $(1,-9)$ . Write its equation in slope-intercept form. $\newline$ 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

(-2,-3)

and

(1,-9)

. Write its equation in slope-intercept form.

\newline

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 $(-2, -3)$ and $(1, -9)$ . $\newline$ To find the slope $m$ , use the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ . $\newline$ Here, $(x_1, y_1) = (-2, -3)$ and $(x_2, y_2) = (1, -9)$ . $\newline$ $m = \frac{-9 - (-3)}{1 - (-2)}$ $\newline$ $m = \frac{-9 + 3}{1 + 2}$ $\newline$ $m = \frac{-6}{3}$ $\newline$ $m = -2$
Find y-intercept: Step $2$ : Use the slope and one point to find the y-intercept $b$ of the line. $\newline$ We have $m = -2$ and we can use point $(1, -9)$ . $\newline$ Substitute into the equation $y = mx + b$ . $\newline$ $-9 = -2(1) + b$ $\newline$ $-9 = -2 + b$ $\newline$ $b = -9 + 2$ $\newline$ $b = -7$
Write equation: Step $3$ : Write the equation of the line in slope-intercept form using the values of $m$ and $b$ . The slope-intercept form is $y = mx + b$ . Substituting $m = -2$ and $b = -7$ , we get: $y = -2x - 7$

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