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:

Which of the following is an equation of the line in the xy-plane that passes through the point (2,6) and is parallel to the line with equation x=(2)/(3)y+2 ? Choose 1 answer: (A) y=-(2)/(3)x+3 (B) y=-(2)/(3)x-3 (C) y=(3)/(2)x+3 (D) y=(3)/(2)x-3

Which of the following is an equation of the line in the xy x y -plane that passes through the point (2,6) (2,6) and is parallel to the line with equation x=23y+2 x=\frac{2}{3} y+2 ?\newlineChoose 11 answer:\newline(A) y=−23x+3 y=-\frac{2}{3} x+3 \newline(B) y=−23x−3 y=-\frac{2}{3} x-3 \newline(C) y=32x+3 y=\frac{3}{2} x+3 \newline(D) y=32x−3 y=\frac{3}{2} x-3

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. Which of the following is an equation of the line in the xy x y -plane that passes through the point (2,6) (2,6) and is parallel to the line with equation x=23y+2 x=\frac{2}{3} y+2 ?\newlineChoose 11 answer:\newline(A) y=−23x+3 y=-\frac{2}{3} x+3 \newline(B) y=−23x−3 y=-\frac{2}{3} x-3 \newline(C) y=32x+3 y=\frac{3}{2} x+3 \newline(D) y=32x−3 y=\frac{3}{2} x-3
  1. Find slope of given line: The question prompt is: ＂What is the equation of the line that passes through the point (2,6)(2,6) and is parallel to the line with equation x=23y+2x=\frac{2}{3}y+2?＂
  2. Parallel line has same slope: First, we need to find the slope of the line that is parallel to the given line. Since parallel lines have the same slope, we can find the slope of the given line by rearranging its equation into slope-intercept form y=mx+by = mx + b.\newlineThe given equation is x=23y+2x = \frac{2}{3}y + 2. To rearrange, we solve for yy:\newlinex−2=23yx - 2 = \frac{2}{3}y\newliney=32x−3y = \frac{3}{2}x - 3\newlineThe slope mm of the given line is 32\frac{3}{2}.
  3. Use point-slope form: Since the line we are looking for is parallel to the given line, it will have the same slope. Therefore, the slope of the line we are looking for is also 32\frac{3}{2}.
  4. Distribute the slope: Now we use the point-slope form of the equation of a line to find the equation of the line that passes through the point (2,6)(2,6) with the slope 32\frac{3}{2}. The point-slope form is given by (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.\newlinePlugging in the point (2,6)(2,6) and the slope 32\frac{3}{2}, we get:\newline(y−6)=(32)(x−2)(y - 6) = \left(\frac{3}{2}\right)(x - 2)
  5. Convert to slope-intercept form: Next, we simplify the equation by distributing the slope on the right side:\newliney - 66 = (32)x−(32)⋅2\left(\frac{3}{2}\right)x - \left(\frac{3}{2}\right)\cdot 2\newliney - 66 = (32)x−3\left(\frac{3}{2}\right)x - 3
  6. Compare with answer choices: To get the equation in slope-intercept form y=mx+by = mx + b, we add 66 to both sides of the equation:\newliney=(32)x−3+6y = \left(\frac{3}{2}\right)x - 3 + 6\newliney=(32)x+3y = \left(\frac{3}{2}\right)x + 3
  7. Compare with answer choices: To get the equation in slope-intercept form y=mx+by = mx + b, we add 66 to both sides of the equation:\newliney=(32)x−3+6y = \left(\frac{3}{2}\right)x - 3 + 6\newliney=(32)x+3y = \left(\frac{3}{2}\right)x + 3Now we compare the equation we found with the answer choices. The equation y=(32)x+3y = \left(\frac{3}{2}\right)x + 3 matches with option (C).

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 9 months ago

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

Posted 9 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 9 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 9 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 9 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 9 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 9 months ago

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

Posted 9 months ago

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

Posted 9 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 9 months ago

View all (101)

Related topics

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