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Complete the equation of the line through (2,-2) and (4,1). Use exact numbers. y=

Complete the equation of the line through (2,−2) (2,-2) and (4,1) (4,1) .\newlineUse exact numbers.\newliney= y=

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Q. Complete the equation of the line through (2,−2) (2,-2) and (4,1) (4,1) .\newlineUse exact numbers.\newliney= y=
  1. Calculate Slope: To find the equation of a line, we need to determine the slope mm of the line using the formula m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}, where (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) are the coordinates of the two given points.\newlineLet's calculate the slope using the points (2,−2)(2, -2) and (4,1)(4, 1).\newlinem=1−(−2)4−2=1+24−2=32m = \frac{1 - (-2)}{4 - 2} = \frac{1 + 2}{4 - 2} = \frac{3}{2}
  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−y1=m(x−x1)y - y_1 = m(x - x_1), where mm is the slope and (x1,y1)(x_1, y_1) is a point on the line.\newlineLet's use the point (2,−2)(2, -2) and the slope 32\frac{3}{2} to write the equation.\newliney−(−2)=(32)(x−2)y - (-2) = \left(\frac{3}{2}\right)(x - 2)
  3. Simplify Equation: Simplify the equation by distributing the slope on the right side and moving the −2-2 to the other side.\newliney+2=(32)x−(32)⋅2y + 2 = \left(\frac{3}{2}\right)x - \left(\frac{3}{2}\right)\cdot2\newliney+2=(32)x−3y + 2 = \left(\frac{3}{2}\right)x - 3\newlineNow, subtract 22 from both sides to isolate yy.\newliney=(32)x−3−2y = \left(\frac{3}{2}\right)x - 3 - 2\newliney=(32)x−5y = \left(\frac{3}{2}\right)x - 5

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