
To solve the system by graphing, plot each line on the same graph and find their intersection point.

For y = -3x + 4y=−3x+4, the y-intercept is 4, and the slope is -3.
For y = 3x - 2y=3x−2, the y-intercept is -2, and the slope is 3.
Plot these lines and see where they intersect. That intersection point is the solution to the system.

To solve the system of equations by graphing, let's break down the process for each line:

### Equations:
1. \( y = -3x + 4 \)
2. \( y = 3x - 2 \)

### Steps:

1. **For the first equation \( y = -3x + 4 \):**
   - The **y-intercept** is 4 (i.e., the point where \( x = 0 \), \( y = 4 \)).
   - The **slope** is -3, meaning for every 1 unit you move right along the x-axis, you move 3 units down along the y-axis.

   So, plot the point \( (0, 4) \) on the graph. From there, use the slope to plot additional points. For example, move 1 unit right (to \( x = 1 \)) and 3 units down (to \( y = 1 \)), giving the point \( (1, 1) \).

2. **For the second equation \( y = 3x - 2 \):**
   - The **y-intercept** is -2 (i.e., the point where \( x = 0 \), \( y = -2 \)).
   - The **slope** is 3, meaning for every 1 unit you move right along the x-axis, you move 3 units up along the y-axis.

   Plot the point \( (0, -2) \) on the graph. From there, use the slope to plot more points. Move 1 unit right (to \( x = 1 \)) and 3 units up (to \( y = 1 \)), giving the point \( (1, 1) \).

### Intersection Point:
Both lines pass through the point \( (1, 1) \), meaning the lines intersect at this point.

Thus, the **solution** to the system of equations is \( \mathbf{(1, 1)} \).

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Would you like more details on graphing or further steps? Here are some follow-up questions to deepen understanding:

1. How do you graph a line when the slope is a fraction?
2. What happens if two lines have the same slope but different y-intercepts?
3. How can you solve a system of equations using substitution or elimination methods?
4. What does it mean when two lines are parallel?
5. How do you know if two lines will intersect at exactly one point?

**Tip:** A quick way to check your work after graphing is to substitute the coordinates of the intersection point into both original equations to verify that it satisfies both.

To solve the system by graphing, plot each line on the same graph and find their intersection point. For y = -3x + 4, the y-intercept is 4, and the slope is -3. For y = 3x - 2, the y-intercept is -2, and the slope is 3. Plot these lines and see where they intersect. That intersection point is the solution to the system.

Learn how to solve the system of equations y = -3x + 4 and y = 3x - 2 by graphing. This step-by-step guide covers graphing techniques, slope-intercept form, and finding the point of intersection. Suitable for students in Grades 8-10.

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