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What is the equation of the line graphed in the xy-plane that passes through the point (-4,-5) and is parallel to the line whose equation is 3x-4y=-8 ? Choose 1 answer: (A) y=-(4)/(3)x+10 (B) y=(3)/(4)x-2 (c) y=(3)/(4)x-8 (D) y=-(4)/(3)x-8

What is the equation of the line graphed in the xy x y -plane that passes through the point (−4,−5) (-4,-5) and is parallel to the line whose equation is 3x−4y=−8 3 x-4 y=-8 ?\newlineChoose 11 answer:\newline(A) y=−43x+10 y=-\frac{4}{3} x+10 \newline(B) y=34x−2 y=\frac{3}{4} x-2 \newline(C) y=34x−8 y=\frac{3}{4} x-8 \newline(D) y=−43x−8 y=-\frac{4}{3} x-8

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Q. What is the equation of the line graphed in the xy x y -plane that passes through the point (−4,−5) (-4,-5) and is parallel to the line whose equation is 3x−4y=−8 3 x-4 y=-8 ?\newlineChoose 11 answer:\newline(A) y=−43x+10 y=-\frac{4}{3} x+10 \newline(B) y=34x−2 y=\frac{3}{4} x-2 \newline(C) y=34x−8 y=\frac{3}{4} x-8 \newline(D) y=−43x−8 y=-\frac{4}{3} x-8
  1. Find Slope: First, we need to find the slope of the line that is parallel to the given line. Since parallel lines have the same slope, we can find the slope of the given line by rewriting its equation in slope-intercept form y=mx+by = mx + b, where mm is the slope.\newlineThe equation of the given line is 3x−4y=−83x - 4y = -8.\newlineTo find the slope, we need to solve for yy.
  2. Solve for Slope: We isolate yy by adding 4y4y to both sides and subtracting 88 from both sides to get:\newline3x=4y−83x = 4y - 8\newlineNow, we divide both sides by 44 to solve for yy:\newline(3/4)x=y−2(3/4)x = y - 2\newliney=(3/4)x+2y = (3/4)x + 2\newlineThe slope of the given line is 3/43/4.\newlineSince the line we are looking for is parallel to this line, its slope will also be 3/43/4.
  3. Point-Slope Form: Next, we use the point-slope form of the equation of a line to find the equation of the line that passes through the point (−4,−5)(-4, -5) with the slope 34\frac{3}{4}. The point-slope form is given by (y−y1)=m(x−x1)(y - y_1) = m(x - x_1), where (x1,y1)(x_1, y_1) is a point on the line and mm is the slope. Here, x1=−4x_1 = -4, y1=−5y_1 = -5, and m=34m = \frac{3}{4}.
  4. Plug in Values: Plugging the values into the point-slope form, we get:\newline(y−(−5))=(34)(x−(−4))(y - (-5)) = \left(\frac{3}{4}\right)(x - (-4))\newlineSimplifying, we have:\newliney+5=(34)(x+4)y + 5 = \left(\frac{3}{4}\right)(x + 4)
  5. Distribute Slope: Now, we distribute the slope (34)(\frac{3}{4}) on the right side of the equation:\newliney+5=(34)x+(34)⋅4y + 5 = (\frac{3}{4})x + (\frac{3}{4})\cdot4\newliney+5=(34)x+3y + 5 = (\frac{3}{4})x + 3
  6. Simplify Equation: To get the equation in slope-intercept form, we subtract 55 from both sides:\newliney=(34)x+3−5y = \left(\frac{3}{4}\right)x + 3 - 5\newliney=(34)x−2y = \left(\frac{3}{4}\right)x - 2
  7. Final Equation: The equation y=34x−2y = \frac{3}{4}x - 2 is in slope-intercept form and has the same slope as the given line, which means it is parallel to the given line and passes through the point (−4,−5)(-4, -5).\newlineThis corresponds to answer choice (B).

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