Math Problem Statement

5y−8=−2(4−x)5𝑦−8=−2(4−𝑥)

Step 2 of 2 :

Find the equation of the line which passes through the point (11,13)(11,13) and is parallel to the given line. Express your answer in slope-intercept form. Simplify your answer.

Solution

Step 1: Solve the given equation for yy

You are given the equation:

5y8=2(4x)5y - 8 = -2(4 - x)

Distribute the 2-2 on the right-hand side:

5y8=8+2x5y - 8 = -8 + 2x

Next, add 88 to both sides to isolate the term with yy:

5y=2x5y = 2x

Now, divide both sides by 5 to solve for yy:

y=25xy = \frac{2}{5}x

This is the equation of the given line in slope-intercept form, y=mx+by = mx + b, where the slope m=25m = \frac{2}{5}.

Step 2: Find the equation of the line parallel to the given line

Since the new line is parallel to the given line, it will have the same slope, m=25m = \frac{2}{5}. Now, use the point (11,13)(11, 13) to find the equation of the line that passes through this point.

We will use the point-slope form of a line:

yy1=m(xx1)y - y_1 = m(x - x_1)

where m=25m = \frac{2}{5}, x1=11x_1 = 11, and y1=13y_1 = 13. Substituting these values into the equation:

y13=25(x11)y - 13 = \frac{2}{5}(x - 11)

Distribute 25\frac{2}{5} on the right-hand side:

y13=25x225y - 13 = \frac{2}{5}x - \frac{22}{5}

Next, add 1313 to both sides to solve for yy. First, express 13 as a fraction with the denominator 5:

y=25x225+655y = \frac{2}{5}x - \frac{22}{5} + \frac{65}{5}

Simplifying:

y=25x+435y = \frac{2}{5}x + \frac{43}{5}

Final Answer

The equation of the line that passes through the point (11,13)(11, 13) and is parallel to the given line is:

y=25x+435y = \frac{2}{5}x + \frac{43}{5}


Would you like more details or have any questions? Here are 5 related problems you can try:

  1. Find the equation of a line that passes through (7,2)(7, -2) and is parallel to y=3x+1y = 3x + 1.
  2. Find the equation of a line passing through (4,5)(4, 5) and perpendicular to y=12x6y = \frac{1}{2}x - 6.
  3. What is the slope of a line parallel to the line y=34x+2y = -\frac{3}{4}x + 2?
  4. Find the slope of a line perpendicular to the line with equation 2x3y=62x - 3y = 6.
  5. Determine the point where the line y=25x+435y = \frac{2}{5}x + \frac{43}{5} intersects the y-axis.

Tip: When two lines are parallel, they always share the same slope.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slope-Intercept Form
Point-Slope Form
Parallel Lines

Formulas

Slope-intercept form: y = mx + b
Point-slope form: y - y1 = m(x - x1)

Theorems

Parallel lines have equal slopes

Suitable Grade Level

Grades 9-10