4−(5y+2x)=7(x−y) slope intercept form 

To convert the equation \( 4 - (5y + 2x) = 7(x - y) \) into slope-intercept form (which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept), follow these steps:

### Step 1: Expand both sides of the equation
Expand the left and right sides:

\[
4 - 5y - 2x = 7x - 7y
\]

### Step 2: Move all terms involving \( y \) to one side
We want to isolate \( y \). First, add \( 5y \) and \( 7y \) to both sides to get all the \( y \)-terms on the right:

\[
4 - 2x = 7x - 7y + 5y
\]

This simplifies to:

\[
4 - 2x = 7x - 2y
\]

### Step 3: Move all terms involving \( x \) and constants to the other side
Now, move the \( x \)-terms and the constant to the right-hand side:

\[
-2x - 7x = -2y - 4
\]

Simplify both sides:

\[
-9x - 4 = -2y
\]

### Step 4: Solve for \( y \)
Divide both sides by \( -2 \) to isolate \( y \):

\[
y = \frac{-9x - 4}{-2}
\]

Simplify the expression:

\[
y = \frac{9}{2}x + 2
\]

### Final Result
The equation in slope-intercept form is:

\[
y = \frac{9}{2}x + 2
\]

### Explanation
- The slope \( m \) is \( \frac{9}{2} \).
- The y-intercept \( b \) is 2.

Would you like more details or have any questions about this?

### 5 Related Questions
1. How can you find the slope between two points on a line?
2. What is the general form of a linear equation?
3. How do you convert from point-slope form to slope-intercept form?
4. What is the meaning of the slope and y-intercept in a real-world context?
5. How do you graph a line given in slope-intercept form?

### Tip
To check your work, substitute known values of \( x \) and \( y \) back into the original equation to ensure both sides are equal.

4−(5y+2x)=7(x−y) slope intercept form

Learn how to convert the equation 4−(5y+2x)=7(x−y) into slope-intercept form with a detailed step-by-step solution. This algebra problem covers key concepts, such as linear equations and the slope-intercept formula y = mx + b. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation