Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

The equation for line qq can be written as y=83x−1y = \frac{8}{3}x - 1. Line rr is perpendicular to line qq and passes through (8,−7)(8,-7). What is the equation of line rr?\newlineWrite the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 1right chevron icon
Write an equation for a parallel or perpendicular lineright chevron icon

Full solution

Q. The equation for line qq can be written as y=83x−1y = \frac{8}{3}x - 1. Line rr is perpendicular to line qq and passes through (8,−7)(8,-7). What is the equation of line rr?\newlineWrite the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
  1. Determine slope of line q: Determine the slope of line q.\newlineThe equation of line q is given as y=83x−1y = \frac{8}{3}x - 1. The slope (mm) of a line in the slope-intercept form y=mx+by = mx + b is the coefficient of xx. Therefore, the slope of line q is 83\frac{8}{3}.
  2. Find slope of line rr: Find the slope of line rr.\newlineSince line rr is perpendicular to line qq, its slope will be the negative reciprocal of the slope of line qq. The negative reciprocal of 83\frac{8}{3} is −38-\frac{3}{8}.
  3. Use point-slope form: Use the point-slope form to find the equation of line rr. We have the slope of line rr −38-\frac{3}{8} and a point through which it passes (8,−7)(8, -7). The point-slope form of a line is (y−y1)=m(x−x1)(y - y_1) = m(x - x_1), where mm is the slope and (x1,y1)(x_1, y_1) is the point on the line. Plugging in the values, we get: (y−(−7))=−38(x−8)(y - (-7)) = -\frac{3}{8}(x - 8)
  4. Simplify to slope-intercept form: Simplify the equation to slope-intercept form.\newlineFirst, distribute the slope on the right side of the equation:\newliney+7=−38x+3y + 7 = -\frac{3}{8}x + 3\newlineNext, subtract 77 from both sides to solve for yy:\newliney=−38x+3−7y = -\frac{3}{8}x + 3 - 7\newliney=−38x−4y = -\frac{3}{8}x - 4

More problems from Write an equation for a parallel or perpendicular line

Question
Does the point (0,4)(0, 4) satisfy the equation y=xy = x??
Get tutor helpright-arrow

Posted 5 months ago

Question
Find the slope of the line y=−4x+25 y = -4x + \frac{2}{5} .
Get tutor helpright-arrow

Posted 5 months ago

Question
Rewrite the following equation in slope-intercept form.\newliney+8=−8(x−10)y + 8 = -8(x - 10)
Get tutor helpright-arrow

Posted 5 months ago

Question
Find the y y -intercept of the line 14x−16y=−10 14x - 16y = -10 .\newlineWrite your answer as an integer or decimal or fraction, not as an ordered pair.
Get tutor helpright-arrow

Posted 5 months ago

Question
Line q q has a slope of −23 \frac{-2}{3} . Line r r is perpendicular to q q . What is the slope of line r r ?
Get tutor helpright-arrow

Posted 5 months ago

Question
Find the slope of the line y+3=−118(x+6)y + 3 = -\frac{1}{18}(x + 6).\newline
Get tutor helpright-arrow

Posted 5 months ago

Question
Line p p has an equation of y=−8x+6 y = -8x + 6 . Line q q , which is perpendicular to line p p , includes the point (2,−2) (2, -2) . What is the equation of line q q ??\newlineWrite the equation in slope-intercept form.
Get tutor helpright-arrow

Posted 5 months ago

Question
Is the graph of this equation a horizontal or vertical line?\newlinex=7x = 7
Get tutor helpright-arrow

Posted 5 months ago

Question
Determine the standard form of the following equation:\newliney=−10x+7 y = -10x + 7
Get tutor helpright-arrow

Posted 5 months ago

Question
A line with a slope of 99 passes through the point (9,9)(9,9). What is its equation in point-slope form?
Get tutor helpright-arrow

Posted 5 months ago

View all (101)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant