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Complete the equation of the line through
(2,1) and
(5,-8).
Use exact numbers.

y=

Complete the equation of the line through $(2,1)$ and $(5,-8)$ . $\newline$ Use exact numbers. $\newline$ $y=$

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Find the roots of factored polynomials

Full solution

Q. Complete the equation of the line through

(2,1)

and

(5,-8)

.

\newline

Use exact numbers.

\newline

y=

Calculate the slope: To find the equation of a line, we need to determine the slope $m$ 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 given points. $\newline$ Let's calculate the slope using the points $(2,1)$ and $(5,-8)$ . $\newline$ $m = \frac{(-8 - 1)}{(5 - 2)}$ $\newline$ $m = \frac{-9}{3}$ $\newline$ $m = -3$
Write the 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 $(2,1)$ and the slope $-3$ to write the equation. $\newline$ $y - 1 = -3(x - 2)$
Distribute the slope: Next, we distribute the slope $-3$ across the $(x - 2)$ term. $\newline$ $y - 1 = -3x + 6$
Solve for y: Finally, we add $1$ to both sides of the equation to solve for $y$ . $\newline$ $y = -3x + 6 + 1$ $\newline$ $y = -3x + 7$

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