Complete the equation of the line through (3,-8) and (6,-4). 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 (3, -8) and (6, -4): m = (-4 - (-8)) / (6 - 3) = (4) / (3) = 4/3Use 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 (3, -8) and the slope 4/3 to write the equation: y - (-8) = (4/3)(x - 3)Simplify the equation: Simplify the equation by distributing the slope on the right side and moving -8 to the other side of the equation: y + 8 = (4/3)x - (4/3)*3 y + 8 = (4/3)x - 4 y = (4/3)x - 4 - 8 y = (4/3)x - 12

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Algebra 2

Find the roots of factored polynomials

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Q. Complete the equation of the line through

(3,-8)

and

(6,-4)

\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 $(3, -8)$ and $(6, -4)$ : $\newline$ $m = \frac{-4 - (-8)}{6 - 3} = \frac{4}{3} = \frac{4}{3}$
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 $(3, -8)$ and the slope $\frac{4}{3}$ to write the equation: $\newline$ $y - (-8) = \left(\frac{4}{3}\right)(x - 3)$
Simplify the equation: Simplify the equation by distributing the slope on the right side and moving $-8$ to the other side of the equation: $\newline$ $y + 8 = \left(\frac{4}{3}\right)x - \left(\frac{4}{3}\right)\cdot3$ $\newline$ $y + 8 = \left(\frac{4}{3}\right)x - 4$ $\newline$ $y = \left(\frac{4}{3}\right)x - 4 - 8$ $\newline$ $y = \left(\frac{4}{3}\right)x - 12$