Questions: Use the given conditions to write an equation for the line in point-slope form and general form. Passing through (3,-8) and perpendicular to the line whose equation is x-5 y-8=0 The equation of the line in point-slope form is (Type an equation. Use integers or fractions for any numbers in the equation.)

Use the given conditions to write an equation for the line in point-slope form and general form. Passing through (3,-8) and perpendicular to the line whose equation is x-5 y-8=0 The equation of the line in point-slope form is (Type an equation. Use integers or fractions for any numbers in the equation.)
Transcript text: Use the given conditions to write an equation for the line in point-slope form and general form. Passing through $(3,-8)$ and perpendicular to the line whose equation is $x-5 y-8=0$ The equation of the line in point-slope form is $\square$ (Type an equation. Use integers or fractions for any numbers in the equation.)
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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: \(m' = -5\).

Step 2: Use the Point-Slope Form

Using the point \((3, -8)\) and the slope \(m' = -5\), the point-slope form is \(y + 8 = -5(x - 3)\).

Step 3: Convert to Slope-Intercept Form

Rearranging the point-slope form to slope-intercept form gives \(y = -5.0x + 7\).

Final Answer:

The equation of the line that is perpendicular to the given line and passes through \((3, -8)\) is \(y = -5.0x + 7\).

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