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A line passes through the points $(-2, -16)$ and $(4 ,20)$ . Write its equation in slope-intercept form.

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Write a linear equation from two points

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Q. A line passes through the points

(-2, -16)

and

(4 ,20)

. Write its equation in slope-intercept form.

Calculate slope: Step $1$ : Calculate the slope of the line using the given points $(-2, -16)$ and $(4, 20)$ . $\newline$ Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ $\newline$ $m = \frac{20 - (-16)}{4 - (-2)}$ $\newline$ $m = \frac{36}{6}$ $\newline$ $m = 6$
Find y-intercept: Step $2$ : Use the slope and one of the points to find the y-intercept, $b$ . Let's use point $(4, 20)$ . $\newline$ Equation form: $y = mx + b$ $\newline$ Substitute $m = 6$ , $x = 4$ , and $y = 20$ . $\newline$ $20 = 6(4) + b$ $\newline$ $20 = 24 + b$ $\newline$ $b = 20 - 24$ $\newline$ $b = -4$
Write equation: Step $3$ : Write the equation of the line in slope-intercept form using the values of $m$ and $b$ . $\newline$ Equation: $y = mx + b$ $\newline$ Substitute $m = 6$ and $b = -4$ . $\newline$ $y = 6x - 4$

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