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What is the equation of the line that passes through the point (-6,3) and has a slope of -(1)/(2) ? Answer:

What is the equation of the line that passes through the point (−6,3) (-6,3) 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 (−6,3) (-6,3) and has a slope of −12 -\frac{1}{2} ?\newlineAnswer:
  1. Identify Equation Form: Identify the slope-intercept form of a line's equation.\newlineThe slope-intercept form of a line's equation is y=mx+by = mx + b, where mm is the slope and bb is the y-intercept.
  2. Find Y-Intercept: Use the given slope and point to find the y-intercept bb. We have the slope mm as −12-\frac{1}{2} and a point (−6,3)(-6,3) that the line passes through. We can substitute these values into the slope-intercept form to find bb. So, 3=−12×(−6)+b3 = -\frac{1}{2} \times (-6) + b.
  3. Solve for b: Solve for b.\newline3=3+b3 = 3 + b\newlineSubtract 33 from both sides to isolate bb.\newlineb=3−3b = 3 - 3\newlineb=0b = 0
  4. Write Line Equation: Write the equation of the line using the slope and y-intercept.\newlineNow that we have the slope m=−12m = -\frac{1}{2} and y-intercept b=0b = 0, we can write the equation of the line.\newlineThe equation is y=−12x+0y = -\frac{1}{2}x + 0, which simplifies to y=−12xy = -\frac{1}{2}x.

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