Studdy AI Logo
Math  /  Algebra

QuestionUse the given conditions to write an equation for the line in point-slope form and in slope-intercept form. Passing through (9,−6)(9,-6) and perpendicular to the line whose equation is y=15x+5y=\frac{1}{5} x+5
Write an equation for the line in point-slope form. □\square (Simplify your answer. Use integers or fractions for any numbers in the equation.) Write an equation for the line in slope-intercept form. □\square (Simplify your answer. Use integers or fractions for any numbers in the equation.)

Studdy Solution

STEP 1

1. We need to find the equation of a line passing through the point (9,−6) (9, -6) .
2. The line is perpendicular to the given line y=15x+5 y = \frac{1}{5}x + 5 .
3. We need to write the equation in both point-slope form and slope-intercept form.

STEP 2

1. Determine the slope of the line perpendicular to the given line.
2. Use the point-slope form to write the equation of the line.
3. Convert the point-slope form equation to slope-intercept form.

STEP 3

Determine the slope of the line perpendicular to the given line.
The slope of the given line is 15 \frac{1}{5} .
For two lines to be perpendicular, the product of their slopes must be −1-1. Let m m be the slope of the line we are trying to find:
m×15=−1 m \times \frac{1}{5} = -1
Solve for m m :
m=−1×5 m = -1 \times 5 m=−5 m = -5
The slope of the line we are looking for is −5 -5 .

STEP 4

Use the point-slope form to write the equation of the line.
The point-slope form of a line is given by:
y−y1=m(x−x1) y - y_1 = m(x - x_1)
Substitute m=−5 m = -5 and the point (9,−6) (9, -6) :
y−(−6)=−5(x−9) y - (-6) = -5(x - 9)
Simplify:
y+6=−5(x−9) y + 6 = -5(x - 9)
This is the equation of the line in point-slope form.

STEP 5

Convert the point-slope form equation to slope-intercept form.
Start with the point-slope form:
y+6=−5(x−9) y + 6 = -5(x - 9)
Distribute the −5-5:
y+6=−5x+45 y + 6 = -5x + 45
Subtract 6 from both sides to solve for y y :
y=−5x+45−6 y = -5x + 45 - 6 y=−5x+39 y = -5x + 39
This is the equation of the line in slope-intercept form.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord