Complete the solution by solving the equation for *y*. Then find the slope and the *y*-intercept of its graph.


4*x* + 5*y*

=

35

4*x* + 5*y* − 
 
=
 
 + 35
 
=

−4*x* + 35



 
5*y*

=

−4*x*

 + 

35

*y*

=

−4

5

*x* + 7

The slope is  and the *y*-intercept is (  ,  ).

Let's complete the solution step by step.

1. **Given equation**:
   \[
   4x + 5y = 35
   \]

2. **Solve for \( y \)**:
   Subtract \( 4x \) from both sides:
   \[
   5y = -4x + 35
   \]
   Now, divide by 5 to isolate \( y \):
   \[
   y = -\frac{4}{5}x + 7
   \]

3. **Identify the slope and y-intercept**:
   The equation is now in the slope-intercept form, \( y = mx + b \), where:
   - \( m = -\frac{4}{5} \) is the slope.
   - \( b = 7 \) is the y-intercept.

   Therefore:
   - The slope is \( -\frac{4}{5} \).
   - The y-intercept is \( (0, 7) \).

**Summary**:
- The slope is \( -\frac{4}{5} \).
- The y-intercept is \( (0, 7) \).

Would you like more details or have any questions? Here are five related questions:

1. How do you find the slope and y-intercept from an equation in standard form?
2. What is the significance of the slope in a linear equation?
3. How can the slope-intercept form be used to graph a linear equation?
4. How would the graph change if the slope were positive instead of negative?
5. What are some real-world applications of slope and y-intercept in equations?

**Tip**: When converting an equation from standard form to slope-intercept form, always isolate the \( y \)-term first.

Complete the solution by solving the equation for y. Then find the slope and the y-intercept of its graph.

4x + 5y = 35

Learn how to solve the linear equation 4x + 5y = 35 and find the slope and y-intercept of its graph. This problem involves converting the equation to slope-intercept form, identifying the slope as -4/5, and the y-intercept as (0, 7). Suitable for Grades 8-10 students studying linear equations.

Math Problem Statement

4x + 5y −

+ 35

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation