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What is the equation of the line that passes through the point (4,-6) and has a slope of (1)/(2) ? Answer:

What is the equation of the line that passes through the point (4,−6) (4,-6) and has a slope of 12 \frac{1}{2} ?\newlineAnswer:

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Q. What is the equation of the line that passes through the point (4,−6) (4,-6) and has a slope of 12 \frac{1}{2} ?\newlineAnswer:
  1. Use Slope-Intercept Form: Use the slope-intercept form y=mx+by = mx + b, where mm is the slope and bb is the y-intercept.
  2. Given Slope and Point: Given slope mm is 12\frac{1}{2} and the point (4,−6)(4, -6) lies on the line.
  3. Plug Values to Solve: Plug x=4x = 4, y=−6y = -6, and m=12m = \frac{1}{2} into the equation y=mx+by = mx + b to solve for bb.\newline−6=(12)×4+b-6 = \left(\frac{1}{2}\right) \times 4 + b
  4. Simplify the Equation: Simplify the equation: −6=2+b-6 = 2 + b.
  5. Subtract to Solve for b: Subtract 22 from both sides to solve for bb: −6−2=b-6 - 2 = b.
  6. Calculate bb: Calculate bb: b=−8b = -8.
  7. Final Equation: Now we have the slope m=12m = \frac{1}{2} and y-intercept b=−8b = -8.
  8. Final Equation: Now we have the slope m=12m = \frac{1}{2} and y-intercept b=−8b = -8.Write the final equation of the line using the values of mm and bb: y=(12)x−8y = \left(\frac{1}{2}\right)x - 8.

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