Complete the equation of the line through (6,-6) and (8,8). 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 (6, -6) and (8, 8). m = (8 - (-6)) / (8 - 6) = 14 / 2 = 7Use 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 (6, -6) and the slope 7 to write the equation. y - (-6) = 7(x - 6)Simplify Equation: Simplify the equation by distributing the slope and moving the -6 to the other side of the equation. y + 6 = 7x - 42 y = 7x - 42 - 6 y = 7x - 48

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Math Problems

Algebra 2

Find the roots of factored polynomials

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Q. Complete the equation of the line through

(6,-6)

and

(8,8)

\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 $(6, -6)$ and $(8, 8)$ . $\newline$ $m = \frac{8 - (-6)}{8 - 6} = \frac{14}{2} = 7$
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 $(6, -6)$ and the slope $7$ to write the equation. $\newline$ $y - (-6) = 7(x - 6)$
Simplify Equation: Simplify the equation by distributing the slope and moving the $-6$ to the other side of the equation. $\newline$ $y + 6 = 7x - 42$ $\newline$ $y = 7x - 42 - 6$ $\newline$ $y = 7x - 48$