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

What is the equation of the line that passes through the point (−6,−2) (-6,-2) and has a slope of −23 -\frac{2}{3} ?\newlineAnswer:

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Q. What is the equation of the line that passes through the point (−6,−2) (-6,-2) and has a slope of −23 -\frac{2}{3} ?\newlineAnswer:
  1. Identify slope and point: Identify the slope and the point through which the line passes. The slope mm is given as −23-\frac{2}{3}, and the point is (−6,−2)(-6, -2).
  2. Use point-slope form: Use the point-slope form of the equation of a line to start.\newlineThe point-slope form is y−y1=m(x−x1)y - y_1 = m(x - x_1), where (x1,y1)(x_1, y_1) is a point on the line and mm is the slope.
  3. Substitute point and slope: Substitute the given point and slope into the point-slope form.\newlineUsing the point (−6,−2)(-6, -2) and the slope −23-\frac{2}{3}, we get:\newliney−(−2)=−23(x−(−6))y - (-2) = -\frac{2}{3}(x - (-6))
  4. Simplify the equation: Simplify the equation. y+2=−23(x+6)y + 2 = -\frac{2}{3}(x + 6)
  5. Distribute the slope: Distribute the slope on the right side of the equation. \newliney+2=−23x−23⋅6y + 2 = -\frac{2}{3}x - \frac{2}{3}\cdot6
  6. Multiply fractions: Multiply the fractions on the right side of the equation. \newliney+2=−23x−4y + 2 = -\frac{2}{3}x - 4
  7. Isolate y: Isolate y to get the equation in slope-intercept form.\newlineSubtract 22 from both sides of the equation:\newliney=−23x−4−2y = -\frac{2}{3}x - 4 - 2\newliney=−23x−6y = -\frac{2}{3}x - 6

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