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QuestionFind the equation of a line in point-slope form that passes through (5,−3)(5,-3) with a slope of −12-\frac{1}{2}.

Studdy Solution

STEP 1

Assumptions1. The line includes the point (5,−3)(5,-3). The slope of the line is −1-\frac{1}{}
3. We need to find the equation of the line in point-slope form

STEP 2

The point-slope form of a line is given by the formulay−y1=m(x−x1)y - y1 = m(x - x1)where (x1,y1)(x1, y1) is a point on the line and mm is the slope of the line.

STEP 3

Now, we can plug in the given values for the point and the slope into the point-slope form equation.
y−(−3)=−12(x−5)y - (-3) = -\frac{1}{2}(x -5)

STEP 4

implify the equation by removing the double negative on the left side of the equation.
y+3=−12(x−)y +3 = -\frac{1}{2}(x -)

STEP 5

Next, distribute the −12-\frac{1}{2} on the right side of the equation.
y+3=−12x+52y +3 = -\frac{1}{2}x + \frac{5}{2}

STEP 6

Finally, subtract3 from both sides of the equation to isolate yy.
y=−12x+52−3y = -\frac{1}{2}x + \frac{5}{2} -3

STEP 7

Convert3 to a fraction with2 as the denominator to simplify the equation.
3=623 = \frac{6}{2}y=−12x+52−62y = -\frac{1}{2}x + \frac{5}{2} - \frac{6}{2}

STEP 8

Subtract the fractions on the right side of the equation.
y=−12x−12y = -\frac{1}{2}x - \frac{1}{2}The equation of the line in point-slope form that includes the point (5,−3)(5,-3) and has a slope of −12-\frac{1}{2} is y=−12x−12y = -\frac{1}{2}x - \frac{1}{2}.

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