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What is the equation of the line that passes through the point (4,-5) and has a slope of -(1)/(4) ? Answer:

What is the equation of the line that passes through the point (4,−5) (4,-5) and has a slope of −14 -\frac{1}{4} ?\newlineAnswer:

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Q. What is the equation of the line that passes through the point (4,−5) (4,-5) and has a slope of −14 -\frac{1}{4} ?\newlineAnswer:
  1. Identify slope and point: Identify the slope and the point through which the line passes. The slope mm is given as −14-\frac{1}{4}, and the point is (4,−5)(4, -5).
  2. Use slope-intercept form: Use the slope-intercept form of a line equation.\newlineThe slope-intercept form is y=mx+by = mx + b, where mm is the slope and bb is the y-intercept.
  3. Substitute values and solve: Substitute the slope and the coordinates of the given point into the slope-intercept equation to solve for bb, the y-intercept.\newlineUsing the point (4,−5)(4, -5), we substitute m=−14m = -\frac{1}{4}, x=4x = 4, and y=−5y = -5 into the equation y=mx+by = mx + b.\newline−5=−14×4+b-5 = -\frac{1}{4} \times 4 + b
  4. Simplify to find bb: Simplify the equation to find the value of bb.−5=−1+b-5 = -1 + b Add 11 to both sides to isolate bb.−5+1=b-5 + 1 = b−4=b-4 = b
  5. Write final equation: Write the final equation of the line using the slope mm and the y-intercept bb. Now that we have b=−4b = -4 and m=−14m = -\frac{1}{4}, we substitute these values into the slope-intercept form. y=−14x−4y = -\frac{1}{4}x - 4

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