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What is the equation of the line that passes through the point (-6,5) and has a slope of -(5)/(3) ? Answer:

What is the equation of the line that passes through the point (−6,5) (-6,5) and has a slope of −53 -\frac{5}{3} ?\newlineAnswer:

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Q. What is the equation of the line that passes through the point (−6,5) (-6,5) and has a slope of −53 -\frac{5}{3} ?\newlineAnswer:
  1. Identify slope and point: Identify the slope and the point through which the line passes. The slope mm is given as −53-\frac{5}{3}, and the point is (−6,5)(-6,5).
  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 and solve for bb: Substitute the slope and the coordinates of the given point into the slope-intercept equation to solve for bb, the y-intercept.\newlineUsing the point (−6,5)(-6,5), we substitute into y=mx+by = mx + b to get:\newline5=(−53)×(−6)+b5 = \left(-\frac{5}{3}\right) \times (-6) + b
  4. Perform multiplication: Perform the multiplication and solve for bb.5=(−53)×(−6)+b5 = \left(-\frac{5}{3}\right) \times (-6) + b5=10+b5 = 10 + b5−10=b5 - 10 = bb=−5b = -5
  5. Write final equation: Write the final equation of the line using the slope mm and the y-intercept bb.\newlineSubstitute m=−53m = -\frac{5}{3} and b=−5b = -5 into y=mx+by = mx + b to get the final equation:\newliney=(−53)x−5y = \left(-\frac{5}{3}\right)x - 5

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