Complete the equation of the line through (2,-2) and (4,1). 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 (2, -2) and (4, 1). m = (1 - (-2)) / (4 - 2) = (1 + 2) / (4 - 2) = 3 / 2Use 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, -2) and the slope 3/2 to write the equation. y - (-2) = (3/2)(x - 2)Simplify Equation: Simplify the equation by distributing the slope on the right side and moving the -2 to the other side. y + 2 = (3/2)x - (3/2)*2 y + 2 = (3/2)x - 3 Now, subtract 2 from both sides to isolate y. y = (3/2)x - 3 - 2 y = (3/2)x - 5

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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

(2,-2)

and

(4,1)

\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 $(2, -2)$ and $(4, 1)$ . $\newline$ $m = \frac{1 - (-2)}{4 - 2} = \frac{1 + 2}{4 - 2} = \frac{3}{2}$
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 $(2, -2)$ and the slope $\frac{3}{2}$ to write the equation. $\newline$ $y - (-2) = \left(\frac{3}{2}\right)(x - 2)$
Simplify Equation: Simplify the equation by distributing the slope on the right side and moving the $-2$ to the other side. $\newline$ $y + 2 = \left(\frac{3}{2}\right)x - \left(\frac{3}{2}\right)\cdot2$ $\newline$ $y + 2 = \left(\frac{3}{2}\right)x - 3$ $\newline$ Now, subtract $2$ from both sides to isolate $y$ . $\newline$ $y = \left(\frac{3}{2}\right)x - 3 - 2$ $\newline$ $y = \left(\frac{3}{2}\right)x - 5$