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A linear equation is graphed. Which of the following equations combin with the graphed equation to create a system of equations whose solut set is comprised of the points (-1,-5) and (3,3) ?

A linear equation is graphed. Which of the following equations combin with the graphed equation to create a system of equations whose solut set is comprised of the points (−1,−5) (-1,-5) and (3,3) (3,3) ?

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Full solution

Q. A linear equation is graphed. Which of the following equations combin with the graphed equation to create a system of equations whose solut set is comprised of the points (−1,−5) (-1,-5) and (3,3) (3,3) ?
  1. Calculate slope: Calculate the slope mm using the given points (−1,−5)(-1,-5) and (3,3)(3,3).m=y2−y1x2−x1=3−(−5)3−(−1)=84=2.m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - (-5)}{3 - (-1)} = \frac{8}{4} = 2.
  2. Find y-intercept: Use one of the points and the slope to find the y-intercept bb. Let's use the point (3,3)(3,3).\newlineSubstitute into y=mx+by = mx + b: 3=2(3)+b3 = 2(3) + b.\newlineSolve for bb: 3=6+b3 = 6 + b; b=3−6b = 3 - 6; b=−3b = -3.
  3. Write equation: Write the equation of the line in slope-intercept form using m=2m = 2 and b=−3b = -3. The equation is y=2x−3y = 2x - 3.

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