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What is the equation of the line that passes through the point (4,0) and has a slope of -(1)/(2) ? Answer:

What is the equation of the line that passes through the point (4,0) (4,0) and has a slope of −12 -\frac{1}{2} ?\newlineAnswer:

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Q. What is the equation of the line that passes through the point (4,0) (4,0) and has a slope of −12 -\frac{1}{2} ?\newlineAnswer:
  1. Identify slope and point: Identify the slope and the point through which the line passes. The slope mm is given as −12-\frac{1}{2}, and the line passes through the point (4,0)(4,0).
  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), where (x1,y1)(x_1, y_1) is a point on the line.\newlineHere, x1=4x_1 = 4 and y1=0y_1 = 0, so we substitute these values into the equation along with the slope m=−12m = -\frac{1}{2}.\newliney−0=−12(x−4)y - 0 = -\frac{1}{2}(x - 4)
  3. Simplify equation to slope-intercept form: Simplify the equation to get it into slope-intercept form, y=mx+by = mx + b.\newliney=−12(x−4)y = -\frac{1}{2}(x - 4)\newliney=−12x+12⋅4y = -\frac{1}{2}x + \frac{1}{2}\cdot 4\newliney=−12x+2y = -\frac{1}{2}x + 2
  4. Check equation for correctness: Check the equation to ensure it is in slope-intercept form and that it represents the correct slope and y-intercept.\newlineThe equation y=−12x+2y = -\frac{1}{2}x + 2 is in slope-intercept form (y=mx+by = mx + b), with m=−12m = -\frac{1}{2} and b=2b = 2. This matches the given slope and the y-intercept can be confirmed by plugging x=4x = 4 into the equation to see if it yields y=0y = 0.\newline−12⋅4+2=−2+2=0-\frac{1}{2}\cdot 4 + 2 = -2 + 2 = 0\newlineSince the point (4,0)(4,0) satisfies the equation, there is no math error.

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