Questions: Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form. Passing through (8,-7) and perpendicular to the line whose equation is y=1/2 x+5

Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form. Passing through (8,-7) and perpendicular to the line whose equation is y=1/2 x+5
Transcript text: Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form. Passing through $(8,-7)$ and perpendicular to the line whose equation is $y=\frac{1}{2} x+5$ Write an equation for the line in point-slope form.
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Solution

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Solution Steps

Step 1: Determine the Slope

The slope of the new line is the negative reciprocal of the given line: \(m' = -2\).

Step 2: Use the Point-Slope Form

Using the point \((8, -7)\) and the slope \(m' = -2\), the point-slope form is \(y + 7 = -2(x - 8)\).

Step 3: Convert to Slope-Intercept Form

Rearranging the point-slope form to slope-intercept form gives \(y = -2.0x + 9\).

Final Answer:

The equation of the line that is perpendicular to the given line and passes through \((8, -7)\) is \(y = -2.0x + 9\).

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