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:

Line vv has an equation of y=−15x+9y = -\frac{1}{5}x + 9. Line ww includes the point (−10,1)(-10,1) and is parallel to line vv. What is the equation of line ww?\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. Line vv has an equation of y=−15x+9y = -\frac{1}{5}x + 9. Line ww includes the point (−10,1)(-10,1) and is parallel to line vv. What is the equation of line ww?\newlineWrite the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.
  1. Find Slope of Line v: Determine the slope of line v. Line v has an equation of y=−15x+9y = -\frac{1}{5}x + 9. The slope-intercept form of a line is y=mx+by = mx + b, where mm is the slope and bb is the y-intercept. Therefore, the slope of line v is −15-\frac{1}{5}.
  2. Determine Parallel Slope: Since line ww is parallel to line vv, it must have the same slope. Parallel lines have the same slope. Therefore, the slope of line ww is also −15-\frac{1}{5}.
  3. Calculate Y-Intercept of Line w: Use the point (−10,1)(-10,1) and the slope −15-\frac{1}{5} to find the y-intercept (b)(b) of line w.\newlineWe can use the point-slope form of the equation of a line, which is y−y1=m(x−x1)y - y_1 = m(x - x_1), where (x1,y1)(x_1, y_1) is a point on the line and mm is the slope. Plugging in the point (−10,1)(-10,1) and the slope −15-\frac{1}{5}, we get:\newline1−y1=−15(x−(−10))1 - y_1 = -\frac{1}{5}(x - (-10))\newline1−y1=−15(x+10)1 - y_1 = -\frac{1}{5}(x + 10)\newlineNow we need to solve for −15-\frac{1}{5}00, which is the y-intercept.
  4. Solve for Y-Intercept: Solve for the y-intercept bb of line ww.1=−15(−10)+b1 = -\frac{1}{5}(-10) + b1=2+b1 = 2 + bSubtract 22 from both sides to isolate bb:1−2=b1 - 2 = b−1=b-1 = bThe y-intercept of line ww is −1-1.
  5. Write Equation of Line w: Write the equation of line w in slope-intercept form.\newlineWe have the slope m=−15m = -\frac{1}{5} and the y-intercept b=−1b = -1. The slope-intercept form is y=mx+by = mx + b. Substituting the values we have:\newliney=−15x−1y = -\frac{1}{5}x - 1\newlineThis is the equation of line w in slope-intercept form.

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 7 months ago

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

Posted 7 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 7 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 7 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 7 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 7 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 7 months ago

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

Posted 7 months ago

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

Posted 7 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 7 months ago

View all (101)

Related topics

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