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What is the equation of the line that passes through the point (-3,-7) and has a slope of -(1)/(3) ? Answer:

What is the equation of the line that passes through the point (−3,−7) (-3,-7) and has a slope of −13 -\frac{1}{3} ?\newlineAnswer:

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Q. What is the equation of the line that passes through the point (−3,−7) (-3,-7) and has a slope of −13 -\frac{1}{3} ?\newlineAnswer:
  1. Identify slope and point: Identify the slope and the point through which the line passes. The slope mm is given as −13-\frac{1}{3}, and the point is (−3,−7)(-3, -7).
  2. Use slope-intercept form: Use the slope-intercept form of a line equation.\newlineThe slope-intercept form is y=mx+by = mx + b, where mm is the slope and bb is the y-intercept.
  3. Substitute slope and point: Substitute the slope and the coordinates of the given point into the equation to find the y-intercept bb. Using the point (−3,−7)(-3, -7), we substitute into the equation: −7=−13×(−3)+b-7 = -\frac{1}{3} \times (-3) + b.
  4. Solve for y-intercept: Solve for bb.−7=1+b-7 = 1 + bSubtract 11 from both sides to isolate bb.−7−1=b-7 - 1 = b−8=b-8 = b
  5. Write final line equation: Write the final equation of the line using the slope and the y-intercept.\newlineNow that we have the slope, m=−13m = -\frac{1}{3}, and the y-intercept, b=−8b = -8, we can write the equation as:\newliney=−13x−8y = -\frac{1}{3}x - 8

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