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

Calculate the slope: To find the equation of a line, we need to determine the slope (m) 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 (2,1) and (5,-8). m = (-8 - 1) / (5 - 2) m = -9 / 3 m = -3Write 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 (2,1) and the slope -3 to write the equation. y - 1 = -3(x - 2)Distribute the slope: Next, we distribute the slope -3 across the (x - 2) term. y - 1 = -3x + 6Solve for y: Finally, we add 1 to both sides of the equation to solve for y. y = -3x + 6 + 1 y = -3x + 7

Home

Math Problems

Algebra 2

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 $y$ . $\newline$ $y = -3x + 6 + 1$ $\newline$ $y = -3x + 7$