https://file.aiquickdraw.com/mathbot/file/17288796682281j18fms9.jpg

The problem provided asks to graph the equation \(2x - 2y = -4\), and then determine the slope, \(m\), as well as the x- and y-intercepts of the line.

Let's solve it step by step:

### Step 1: Rewrite the equation in slope-intercept form
We start by solving the equation \(2x - 2y = -4\) for \(y\) to get the equation into the slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

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

First, subtract \(2x\) from both sides:

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

Next, divide every term by \(-2\):

\[
y = x + 2
\]

Now, the equation is in slope-intercept form \(y = x + 2\), where the slope \(m = 1\) and the y-intercept is \(2\).

### Step 2: Determine the x- and y-intercepts
- **Y-intercept**: The y-intercept is where the line crosses the y-axis, which occurs when \(x = 0\). From the equation \(y = x + 2\):
  \[
  y = 0 + 2 = 2
  \]
  So, the y-intercept is \( (0, 2) \).

- **X-intercept**: The x-intercept is where the line crosses the x-axis, which occurs when \(y = 0\). Set \(y = 0\) in the equation \(y = x + 2\):
  \[
  0 = x + 2
  \]
  Solving for \(x\):
  \[
  x = -2
  \]
  So, the x-intercept is \( (-2, 0) \).

### Step 3: Graph the line
1. Label the axes.
2. Plot the x-intercept \( (-2, 0) \) and the y-intercept \( (0, 2) \).
3. Draw a straight line through these two points.

### Summary:
- **Slope (m)**: 1
- **X-intercept**: \( (-2, 0) \)
- **Y-intercept**: \( (0, 2) \)

Would you like further details or have any questions about these steps?

Here are some related questions to explore further:
1. What does the slope represent in a real-world context?
2. How can you find the equation of a line given two points?
3. How would the graph change if the equation was \(2x + 2y = -4\)?
4. Can you describe how to find the distance between two points on this line?
5. What happens to the slope when the coefficients of \(x\) and \(y\) are modified?

**Tip**: Always verify the slope visually on the graph by checking the rise over run between two points.

In your notes for this problem, draw and label a set of axes, then graph the equation 2x - 2y = -4. Finally, determine the slope, m, of the resultant line and the x- and y-intercepts.

Learn how to graph the linear equation 2x - 2y = -4, and find its slope and intercepts. Step-by-step solution suitable for students in Grades 8-10. Discover key algebraic concepts like slope, x- and y-intercepts.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation