Q. Complete the point-slope equation of the line through (−4,8) and (4,4). Use exact numbers.y−4=
Calculate Slope: To find the point-slope form of the equation of the line, we first need to calculate the slopem of the line using the two given points (−4,8) and (4,4). The slope is given by the formula m=x2−x1y2−y1, where (x1,y1) and (x2,y2) are the coordinates of the two points.Calculation: m=4−(−4)4−8=8−4=−21
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 y−y1=m(x−x1), where m is the slope and (x1,y1) 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).Calculation: y−4=(−21)(x−4)
Finalize Equation: We have now written the equation in point-slope form using the point (4,4) and the slope −21. 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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