Question

Use the given conditions to write an equation for the line in point-slope form and general form.

Passing through (2,-3) and perpendicular to the line whose equation is x-5y-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.)

Answer 1

• y +3 = -5(x -2) . . . point-slope form
• 5x +y -7 = 0 . . . . . general form

Explanation:

You want the equation for a line through (2, -3) perpendicular to the line x -5y -8 = 0, written in point-slope form and in general form.

Slope

The slope of the given line can be found by solving for y:

x -8 = 5y

1/5x -8/5 = y

This tells us the given line has a slope of 1/5. That means the perpendicular line's slope will be the opposite reciprocal, or ...

m = -1/(1/5) = -5

Point-slope equation

The equation for a line with slope m through point (h, k) is ...

y -k = m(x -h)

Then the desired line is ...

y +3 = -5(x -2) . . . . . . . line with slope -5 through point (2, -3)

General form

Making the right side of the equation be zero will give the desired form.

y +3 +5(x -2) = 0

5x +y -7 = 0 . . . . . . . . simplify to general form

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