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Complete the point-slope equation of the line through 
(-4,8) and 
(4,4).
Use exact numbers.

y-4=

Complete the point-slope equation of the line through (4,8)(-4,8) and (4,4)(4,4). Use exact numbers.\newliney4=y-4=

Full solution

Q. Complete the point-slope equation of the line through (4,8)(-4,8) and (4,4)(4,4). Use exact numbers.\newliney4=y-4=
  1. Calculate Slope: To find the point-slope form of the equation of the line, we first need to calculate the slope mm of the line using the two given points (4,8)(-4,8) and (4,4)(4,4). The slope is given by the formula m=y2y1x2x1m = \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 points.\newlineCalculation: m=484(4)=48=12m = \frac{4 - 8}{4 - (-4)} = \frac{-4}{8} = -\frac{1}{2}
  2. Write Point-Slope Equation: Now that we have the slope, we can use one of the points and the slope to write the equation in point-slope form. The point-slope form is given by yy1=m(xx1)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. We can use either of the two points, but for this example, let's use the point (4,4)(4,4).\newlineCalculation: y4=(12)(x4)y - 4 = \left(-\frac{1}{2}\right)(x - 4)
  3. Finalize Equation: We have now written the equation in point-slope form using the point (4,4)(4,4) and the slope 12-\frac{1}{2}. There is no need for further simplification as we are asked to use exact numbers and the equation is already in the correct form.

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