For the equation 

4 x minus 7 y equals 284x−7y=28​, 

​(a) write it in​ slope-intercept form, ​(b) give the slope of the​ line, ​(c) give the​ y-intercept, and ​(d) graph the line.

Question content area bottom left

Part 1

​(a)

 yequals=enter your response here




Let's work through the problem step by step.

### Given Equation:
\[ 4x - 7y = 28 \]

### (a) Write it in slope-intercept form (\( y = mx + b \)):

To convert the equation into slope-intercept form, we need to solve for \( y \).

\[
4x - 7y = 28
\]

Subtract \( 4x \) from both sides:

\[
-7y = -4x + 28
\]

Now, divide every term by \(-7\) to solve for \( y \):

\[
y = \frac{4}{7}x - 4
\]

So, the equation in slope-intercept form is:

\[
y = \frac{4}{7}x - 4
\]

### (b) Slope of the line:

In the slope-intercept form \( y = mx + b \), the coefficient of \( x \) is the slope \( m \).

So, the slope \( m \) is:

\[
\text{slope} = \frac{4}{7}
\]

### (c) Y-intercept:

The y-intercept \( b \) is the constant term in the slope-intercept form.

Here, the y-intercept is:

\[
\text{y-intercept} = -4
\]

### (d) Graph the line:

To graph the line, you can plot the y-intercept \( (0, -4) \) and then use the slope \( \frac{4}{7} \) to find another point. Starting from \( (0, -4) \), you move up 4 units and to the right 7 units to plot the next point.

Would you like me to generate the graph for you?

---

If you have any questions or want further details, feel free to ask! Here are 5 related questions for you to consider:

1. How do you determine the slope from two points on a line?
2. What does the slope of a line represent geometrically?
3. How do you find the x-intercept of a line?
4. What happens to the graph of a line if the slope is negative?
5. How can you check if a point lies on a given line?

**Tip:** When converting an equation to slope-intercept form, always isolate the \( y \) term by dividing or multiplying as necessary.

For the equation 4x - 7y = 28, (a) write it in slope-intercept form, (b) give the slope of the line, (c) give the y-intercept, and (d) graph the line.

Learn how to convert the linear equation 4x - 7y = 28 into slope-intercept form, find the slope, determine the y-intercept, and graph the line. This problem is suitable for students in Grades 8-10 and covers essential algebraic concepts related to linear equations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation