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Complete the equation of the line through
(-6,-5) and
(-4,-4). Use exact numbers.

y=

Complete the equation of the line through $(-6,-5)$ and $(-4,-4)$ . Use exact numbers. $\newline$ $y=$

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Solve a quadratic equation using square roots

Full solution

Q. Complete the equation of the line through

(-6,-5)

and

(-4,-4)

. Use exact numbers.

\newline

y=

Calculate Slope: To find the equation of a line, we 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. $\newline$ Using the points $(-6,-5)$ and $(-4,-4)$ , we calculate the slope as follows: $\newline$ $m = \frac{-4 - (-5)}{-4 - (-6)}$ $\newline$ $m = \frac{1}{2}$ $\newline$ $m = \frac{1}{2}$
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. We can use either of the given points; let's use the point $(-6, -5)$ . The equation becomes $y - (-5) = \frac{1}{2}(x - (-6))$ .
Simplify Equation: Simplify the equation by distributing the slope and moving $-5$ to the other side of the equation. $\newline$ $y + 5 = \left(\frac{1}{2}\right)x + 3$ $\newline$ $y = \left(\frac{1}{2}\right)x + 3 - 5$ $\newline$ $y = \left(\frac{1}{2}\right)x - 2$

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