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What is the equation of the line that passes through the point (5,0) and has a slope of -(6)/(5) ? Answer:

What is the equation of the line that passes through the point (5,0) (5,0) and has a slope of −65 -\frac{6}{5} ?\newlineAnswer:

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Full solution

Q. What is the equation of the line that passes through the point (5,0) (5,0) and has a slope of −65 -\frac{6}{5} ?\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 −65-\frac{6}{5}, and the point is (5,0)(5,0).
  2. Use point-slope form: Use the point-slope form of the equation of a line to plug in the values.\newlineThe point-slope form is y−y1=m(x−x1)y - y_1 = m(x - x_1).\newlineHere, y1=0y_1 = 0, x1=5x_1 = 5, and m=−65m = -\frac{6}{5}.
  3. Substitute values: Substitute the values into the point-slope form equation.\newliney−0=−65(x−5)y - 0 = -\frac{6}{5}(x - 5)\newlineThis simplifies to y=−65x+65⋅5y = -\frac{6}{5}x + \frac{6}{5}\cdot 5
  4. Simplify equation: Simplify the equation.\newliney=−65x+6y = -\frac{6}{5}x + 6\newlineThis is the equation of the line in slope-intercept form, where the y-intercept (bb) is 66.

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