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Which of the following equations represents a line that passes through the points (4,12) and (0,-8) ? I. y-17=5(x-5) II. y=-5x-8 Neither I only II only I and II

Which of the following equations represents a line that passes through the points (4,12) (4,12) and (0,−8) (0,-8) ?\newlineI. y−17=5(x−5) y-17=5(x-5) \newlineII. y=−5x−8 y=-5 x-8 \newlineNeither\newlineI only\newlineII only\newlineI and II

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Q. Which of the following equations represents a line that passes through the points (4,12) (4,12) and (0,−8) (0,-8) ?\newlineI. y−17=5(x−5) y-17=5(x-5) \newlineII. y=−5x−8 y=-5 x-8 \newlineNeither\newlineI only\newlineII only\newlineI and II
  1. Calculate slope: Find the slope of the line passing through the points (4,12)(4,12) and (0,−8)(0,-8). The slope mm is calculated using the formula m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}. Here, (x1,y1)=(4,12)(x_1, y_1) = (4, 12) and (x2,y2)=(0,−8)(x_2, y_2) = (0, -8). m=−8−120−4=−20−4=5m = \frac{-8 - 12}{0 - 4} = \frac{-20}{-4} = 5.
  2. Write point-slope equation: Use the slope and one of the points to write the equation of the line in point-slope form.\newlineWe can use the point (4,12)(4, 12) and the slope 55.\newlineThe point-slope form is y−y1=m(x−x1)y - y_1 = m(x - x_1).\newlineSubstituting the values, we get y−12=5(x−4)y - 12 = 5(x - 4).
  3. Convert to slope-intercept form: Convert the point-slope form to slope-intercept form y=mx+by = mx + b to find the y-intercept bb.y−12=5(x−4)y - 12 = 5(x - 4)y=5x−20+12y = 5x - 20 + 12y=5x−8.y = 5x - 8.
  4. Check equation I: Check if equation I, y−17=5(x−5)y - 17 = 5(x - 5), represents the line.\newlineSubstitute x=4x = 4 and y=12y = 12 into the equation.\newline12−17=5(4−5)12 - 17 = 5(4 - 5)\newline−5=5(−1)-5 = 5(-1)\newline−5=−5-5 = -5, which is true.\newlineNow, substitute x=0x = 0 and y=−8y = -8 into the equation.\newline−8−17=5(0−5)-8 - 17 = 5(0 - 5)\newline−25=−25-25 = -25, which is also true.\newlineBoth points satisfy equation I, so it represents the line.
  5. Check equation II: Check if equation II, y=−5x−8y = -5x - 8, represents the line.\newlineSubstitute x=4x = 4 and y=12y = 12 into the equation.\newline12=−5(4)−812 = -5(4) - 8\newline12=−20−812 = -20 - 8\newline12=−2812 = -28, which is not true.\newlineTherefore, equation II does not represent the line.
  6. Determine correct answer: Determine the correct answer based on the checks from steps 44 and 55.\newlineEquation II represents the line, but equation IIII does not.\newlineTherefore, the correct answer is ＂II only＂.

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