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Complete the equation of the line through (3,−8)(3, -8) and (6,−4)(6, -4). Use exact numbers. У=У =

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Full solution

Q. Complete the equation of the line through (3,−8)(3, -8) and (6,−4)(6, -4). Use exact numbers. У=У =
  1. Find slope using formula: First, find the slope mm of the line using the slope formula m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1} where (x1,y1)=(3,−8)(x_1, y_1) = (3, -8) and (x2,y2)=(6,−4)(x_2, y_2) = (6, -4).
  2. Calculate slope: So, m=(−4−(−8))/(6−3)=(−4+8)/3=4/3m = (-4 - (-8)) / (6 - 3) = (-4 + 8) / 3 = 4 / 3.
  3. Use point-slope form: Now, use the point-slope form of the equation of a line, y−y1=m(x−x1)y - y_1 = m(x - x_1), with one of the points, say (3,−8)(3, -8), and the slope 43\frac{4}{3}.
  4. Plug in values: Plug in the values: y−(−8)=(43)(x−3)y - (-8) = \left(\frac{4}{3}\right)(x - 3).
  5. Simplify equation: Simplify the equation: y+8=(43)x−(43)⋅3y + 8 = \left(\frac{4}{3}\right)x - \left(\frac{4}{3}\right)\cdot3.
  6. Further simplify: Further simplify: y+8=(43)x−4y + 8 = \left(\frac{4}{3}\right)x - 4.
  7. Isolate yy: Subtract 88 from both sides to get yy by itself: y=43x−4−8y = \frac{4}{3}x - 4 - 8.
  8. Combine like terms: Combine like terms: y=43x−12y = \frac{4}{3}x - 12.

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