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

What is the equation of the line that passes through the point (6,−6) (6,-6) and has a slope of −16 -\frac{1}{6} ?\newlineAnswer:

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Q. What is the equation of the line that passes through the point (6,−6) (6,-6) and has a slope of −16 -\frac{1}{6} ?\newlineAnswer:
  1. Identify Slope and Point: Identify the slope mm and the point (x1,y1)(x_1, y_1) through which the line passes.\newlineThe slope mm is given as −16-\frac{1}{6}, and the point (x1,y1)(x_1, y_1) is (6,−6)(6, -6).
  2. Use Point-Slope Form: Use the point-slope form of the equation of a line to plug in the values of the slope and the point.\newlineThe point-slope form is y−y1=m(x−x1)y - y_1 = m(x - x_1).\newlineSubstitute m=−16m = -\frac{1}{6}, x1=6x_1 = 6, and y1=−6y_1 = -6 into the equation to get y−(−6)=−16(x−6)y - (-6) = -\frac{1}{6}(x - 6).
  3. Simplify Equation: Simplify the equation from the point-slope form to the slope-intercept form y=mx+by = mx + b. Start by distributing the slope on the right side of the equation: y+6=−16x+16⋅6y + 6 = -\frac{1}{6}x + \frac{1}{6}\cdot6.
  4. Isolate y: Continue simplifying the equation by performing the multiplication on the right side.\newlineThe equation becomes y+6=−16x+1y + 6 = -\frac{1}{6}x + 1.
  5. Combine Like Terms: Isolate yy to get the equation in slope-intercept form.\newlineSubtract 66 from both sides of the equation to get y=−16x+1−6y = -\frac{1}{6}x + 1 - 6.
  6. Combine Like Terms: Isolate yy to get the equation in slope-intercept form.\newlineSubtract 66 from both sides of the equation to get y=−16x+1−6y = -\frac{1}{6}x + 1 - 6.Combine like terms on the right side of the equation to find the y-intercept (b)(b).\newlineThe equation simplifies to y=−16x−5y = -\frac{1}{6}x - 5.

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