Complete the equation of the line through (-1,6) and (7,-2). Use exact numbers. y=◻

Calculate the 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 points the line passes through. Let's calculate the slope using the points (-1, 6) and (7, -2). m = (-2 - 6) / (7 - (-1)) m = (-8) / (8) m = -1Write 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 - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Let's use the point (-1, 6) and the slope -1 to write the equation. y - 6 = -1(x - (-1)) y - 6 = -1(x + 1)Simplify the equation: Next, we simplify the equation by distributing the slope -1 across the terms in the parentheses. y - 6 = -1 * x - 1 * 1 y - 6 = -x - 1Convert to slope-intercept form: To write the equation in slope-intercept form (y = mx + b), we need to solve for y. y = -x - 1 + 6 y = -x + 5

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Algebra 2

Find the roots of factored polynomials

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Q. Complete the equation of the line through

(-1,6)

and

(7,-2)

\newline

Use exact numbers.

\newline

y=\square

Calculate the 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. $\newline$ Let's calculate the slope using the points $(-1, 6)$ and $(7, -2)$ . $\newline$ $m = \frac{(-2 - 6)}{(7 - (-1))}$ $\newline$ $m = \frac{(-8)}{(8)}$ $\newline$ $m = -1$
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 $(-1, 6)$ and the slope $-1$ to write the equation. $\newline$ $y - 6 = -1(x - (-1))$ $\newline$ $y - 6 = -1(x + 1)$
Simplify the equation: Next, we simplify the equation by distributing the slope $-1$ across the terms in the parentheses. $\newline$ $y - 6 = -1 \times x - 1 \times 1$ $\newline$ $y - 6 = -x - 1$
Convert to slope-intercept form: To write the equation in slope-intercept form $y = mx + b$ , we need to solve for $y$ .
$y = -x - 1 + 6$
$y = -x + 5$