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

What is the equation of the line that passes through the point (2,2) (2,2) and has a slope of −32 -\frac{3}{2} ?\newlineAnswer:

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Q. What is the equation of the line that passes through the point (2,2) (2,2) and has a slope of −32 -\frac{3}{2} ?\newlineAnswer:
  1. Identify Slope-Intercept 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 −32-\frac{3}{2} and a point (2,2)(2,2) through which the line passes. We can substitute these values into the slope-intercept form to find bb. Using the point (2,2)(2,2), we get: 2=−32×2+b2 = -\frac{3}{2} \times 2 + b 2=−3+b2 = -3 + b b=2+3b = 2 + 3 b=5b = 5
  3. Write Line Equation: Write the equation of the line using the slope and y-intercept.\newlineNow that we have the slope m=−32m = -\frac{3}{2} and the y-intercept b=5b = 5, we can write the equation of the line.\newlineThe equation is y=−32x+5y = -\frac{3}{2}x + 5.

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