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Graph a line that has a slope of −34-\frac{3}{4} and includes the point (−3,2)(-3,2)

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Full solution

Q. Graph a line that has a slope of −34-\frac{3}{4} and includes the point (−3,2)(-3,2)
  1. Find Slope-Intercept Form: Find the slope-intercept form of the equation using the slope and the given point.\newliney−y1=m(x−x1)y - y_1 = m(x - x_1), where mm is the slope and (x1,y1)(x_1, y_1) is the point.\newliney−2=(−34)(x−(−3))y - 2 = \left(-\frac{3}{4}\right)(x - (-3))
  2. Simplify Equation by Distributing: Simplify the equation by distributing the slope. y−2=(−34)(x+3)y - 2 = \left(-\frac{3}{4}\right)(x + 3)
  3. Multiply Slope with Terms: Multiply the slope with each term inside the parentheses.\newliney−2=(−34)x−(34)(3)y - 2 = \left(-\frac{3}{4}\right)x - \left(\frac{3}{4}\right)(3)
  4. Multiply −34-\frac{3}{4} by 33: Multiply −34-\frac{3}{4} by 33 to get −94-\frac{9}{4}.\newliney−2=(−34)x−94y - 2 = \left(-\frac{3}{4}\right)x - \frac{9}{4}
  5. Add 22 to Both Sides: Add 22 to both sides to get yy by itself.\newliney=(−34)x−94+2y = \left(-\frac{3}{4}\right)x - \frac{9}{4} + 2
  6. Convert 22 to Fraction: Convert 22 to a fraction with the same denominator as −94-\frac{9}{4} to combine the terms.\newliney=(−34)x−94+84y = \left(-\frac{3}{4}\right)x - \frac{9}{4} + \frac{8}{4}
  7. Combine Constant Terms: Combine the constant terms.\newliney=(−34)x−14y = \left(-\frac{3}{4}\right)x - \frac{1}{4}

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