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.

### Step 1: Solve the given equation for \(y\)
You are given the equation:

\[
5y - 8 = -2(4 - x)
\]

Distribute the \(-2\) on the right-hand side:

\[
5y - 8 = -8 + 2x
\]

Next, add \(8\) to both sides to isolate the term with \(y\):

\[
5y = 2x
\]

Now, divide both sides by 5 to solve for \(y\):

\[
y = \frac{2}{5}x
\]

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

### 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, \(m = \frac{2}{5}\). Now, use the point \( (11, 13) \) to find the equation of the line that passes through this point.

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

\[
y - y_1 = m(x - x_1)
\]

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

\[
y - 13 = \frac{2}{5}(x - 11)
\]

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

\[
y - 13 = \frac{2}{5}x - \frac{22}{5}
\]

Next, add \(13\) to both sides to solve for \(y\). First, express 13 as a fraction with the denominator 5:

\[
y = \frac{2}{5}x - \frac{22}{5} + \frac{65}{5}
\]

Simplifying:

\[
y = \frac{2}{5}x + \frac{43}{5}
\]

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

\[
y = \frac{2}{5}x + \frac{43}{5}
\]

---

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

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

Find the equation of the line which passes through the point (11, 13) and is parallel to the given line 5y - 8 = -2(4 - x). Express your answer in slope-intercept form. Simplify your answer.

Discover how to find the equation of a line parallel to 5y - 8 = -2(4 - x) that passes through the point (11, 13). This algebra problem demonstrates the use of slope-intercept and point-slope forms, focusing on concepts like parallel lines. Suitable for Grades 9-10 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation