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Complete the equation of the line through (-9,7) and (-6,-3). Use exact numbers. y=

Complete the equation of the line through (−9,7) (-9,7) and (−6,−3) (-6,-3) . Use exact numbers.\newliney= y=

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Q. Complete the equation of the line through (−9,7) (-9,7) and (−6,−3) (-6,-3) . Use 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 (−9,7)(-9,7) and (−6,−3)(-6,-3):\newlinem=−3−7−6−(−9)m = \frac{-3 - 7}{-6 - (-9)}\newlinem=−103m = \frac{-10}{3}\newlinem=−103m = -\frac{10}{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−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 (−9,7)(-9,7) and the slope −103-\frac{10}{3} to write the equation:\newliney−7=(−103)(x−(−9))y - 7 = (-\frac{10}{3})(x - (-9))\newliney−7=(−103)(x+9)y - 7 = (-\frac{10}{3})(x + 9)
  3. Distribute Slope: Next, we distribute the slope −103-\frac{10}{3} across the terms in the parentheses:\newliney−7=(−103)x−(103)(9)y - 7 = \left(-\frac{10}{3}\right)x - \left(\frac{10}{3}\right)(9)\newliney−7=(−103)x−30y - 7 = \left(-\frac{10}{3}\right)x - 30
  4. Solve for y: Finally, we add 77 to both sides of the equation to solve for yy: \newliney=(−103)x−30+7y = \left(-\frac{10}{3}\right)x - 30 + 7\newliney=(−103)x−23y = \left(-\frac{10}{3}\right)x - 23

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