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Complete the equation of the line through
(-6,5) and
(-3,-3). Use exact numbers.

y=

Complete the equation of the line through $(-6,5)$ and $(-3,-3)$ . Use exact numbers. $\newline$ $y=\square \underline{+}+\underline{\underline{x}}$

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Write a linear equation from two points

Full solution

Q. Complete the equation of the line through

(-6,5)

and

(-3,-3)

. Use exact numbers.

\newline

y=\square \underline{+}+\underline{\underline{x}}

Calculate Slope: To find the equation of a line, we first need to determine the slope $m$ of the line 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 $(-6,5)$ and $(-3,-3)$ . $\newline$ $m = \frac{-3 - 5}{-3 - (-6)}$ $\newline$ $m = \frac{-8}{3}$ $\newline$ $m = -\frac{8}{3}$
Use Point-Slope Form: Now that we have the slope, we can use the point-slope form of the equation of a line, which 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 $(-6,5)$ and the slope $-\frac{8}{3}$ to write the equation. $\newline$ $y - 5 = (-\frac{8}{3})(x - (-6))$ $\newline$ $y - 5 = (-\frac{8}{3})(x + 6)$
Distribute Slope: Next, we distribute the slope $-\frac{8}{3}$ across the terms in the parentheses. $\newline$ $y - 5 = \left(-\frac{8}{3}\right)x - \left(\frac{8}{3}\right)(6)$ $\newline$ $y - 5 = \left(-\frac{8}{3}\right)x - 16$
Solve for y: Finally, we add $5$ to both sides of the equation to solve for $y$ in terms of $x$ . $\newline$ $y = \frac{-8}{3}x - 16 + 5$ $\newline$ $y = \frac{-8}{3}x - 11$

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