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Complete the equation of the line through
(-8,-2) and
(-4,6). Use exact numbers.

y=

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

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Find the roots of factored polynomials

Full solution

Q. Complete the equation of the line through

(-8,-2)

and

(-4,6)

. Use exact numbers.

\newline

y=\square

Finding the Slope: To find the equation of a line, we need to determine the slope ( $m$ ) and the y-intercept ( $b$ ) of the line. The slope can be found using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ , where $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the two points the line passes through. $\newline$ Let's calculate the slope using the points $(-8, -2)$ and $(-4, 6)$ . $\newline$ $m = \frac{6 - (-2)}{-4 - (-8)}$ $\newline$ $m = \frac{6 + 2}{-4 + 8}$ $\newline$ $m = \frac{8}{4}$ $\newline$ $b$ $0$
Using Point-Slope Form: Now that we have the slope, we can use point-slope form to write the equation of the line. The point-slope form is $y - y_1 = m(x - x_1)$ , where $m$ is the slope and $(x_1, y_1)$ is a point on the line. $\newline$ Let's use the point $(-8, -2)$ and the slope $m = 2$ to write the equation. $\newline$ $y - (-2) = 2(x - (-8))$ $\newline$ $y + 2 = 2(x + 8)$ $\newline$ $y + 2 = 2x + 16$
Converting to Slope-Intercept Form: To write the equation in slope-intercept form $y = mx + b$ , we need to isolate $y$ on one side of the equation. $\newline$ Subtract $2$ from both sides to get $y$ by itself. $\newline$ $y = 2x + 16 - 2$ $\newline$ $y = 2x + 14$

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