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Complete the equation of the line through $(-8,-2)$ and $(-4,6)$ . Use exact numbers. $\newline$ $y=\square$

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Write a linear equation from two points

Full solution

Q. Complete the equation of the line through

(-8,-2)

and

(-4,6)

. Use exact numbers.

\newline

y=\square

Given points: Given points: $\newline$ $(-8, -2)$ and $\newline$ $(-4, 6)$ $\newline$ Find the slope of the line using the points. $\newline$ Slope, $m$ $\newline$ $= \frac{y_2 - y_1}{x_2 - x_1}$ $\newline$ $= \frac{6 - (-2)}{-4 - (-8)}$ $\newline$ $= \frac{8}{4}$ $\newline$ $= 2$ $\newline$ So, $m = 2$
Find slope: We have: $\newline$ $m: 2$ $\newline$ Choose one of the points to find the value of $b$ , the y-intercept. Let's use the point $(-8, -2)$ . $\newline$ Substitute $x = -8$ , $y = -2$ , and $m = 2$ in $y = mx + b$ . $\newline$ $-2 = 2(-8) + b$ $\newline$ $-2 = -16 + b$ $\newline$ $-2 + 16 = b$ $\newline$ $b$ $0$ $\newline$ So, $b$ $1$
Find y-intercept: We found: $\newline$ $m: 2$ $\newline$ $b: 14$ $\newline$ Write the equation of the line in slope-intercept form. $\newline$ Substitute $m = 2$ and $b = 14$ in $y = mx + b$ . $\newline$ $y = 2x + 14$ $\newline$ Slope-intercept form: $y = 2x + 14$

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