Complete the equation of the line through (4,-8) and (8,5). Use exact numbers. y=

Calculate slope: To find the equation of a line, we need to determine the slope (m) of the line using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two given points. Let's calculate the slope using the points (4, -8) and (8, 5). m = (5 - (-8)) / (8 - 4) = 13 / 4Use 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 - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Let's use the point (4, -8) and the slope 13/4 to write the equation. y - (-8) = (13/4)(x - 4)Simplify the equation: Simplify the equation by distributing the slope on the right side and moving the -8 to the other side of the equation. y + 8 = (13/4)x - (13/4)*4 y + 8 = (13/4)x - 13 y = (13/4)x - 13 - 8 y = (13/4)x - 21

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Algebra 2

Find the roots of factored polynomials

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Q. Complete the equation of the line through

(4,-8)

and

(8,5)

\newline

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 given points. $\newline$ Let's calculate the slope using the points $(4, -8)$ and $(8, 5)$ . $\newline$ $m = \frac{5 - (-8)}{8 - 4} = \frac{13}{4}$
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 $(4, -8)$ and the slope $\frac{13}{4}$ to write the equation. $\newline$ $y - (-8) = \left(\frac{13}{4}\right)(x - 4)$
Simplify the equation: Simplify the equation by distributing the slope on the right side and moving the $-8$ to the other side of the equation. $\newline$ $y + 8 = \left(\frac{13}{4}\right)x - \left(\frac{13}{4}\right)\cdot4$ $\newline$ $y + 8 = \left(\frac{13}{4}\right)x - 13$ $\newline$ $y = \left(\frac{13}{4}\right)x - 13 - 8$ $\newline$ $y = \left(\frac{13}{4}\right)x - 21$