Question

On a graph plot y = -3x + 4 + y = 3x - 2

Answer 1

To plot the equations \( y = -3x + 4 \) and \( y = 3x - 2 \), we first find points for each line and then graph them.

### Equation 1: \( y = -3x + 4 \)

1. **Y-intercept**: Set \( x = 0 \):
\[
y = -3(0) + 4 = 4 \quad \text{(Point: (0, 4))}
\]

2. **X-intercept**: Set \( y = 0 \):
\[
0 = -3x + 4 \quad \Rightarrow \quad 3x = 4 \quad \Rightarrow \quad x = \frac{4}{3} \quad \text{(Point: (4/3, 0))}
\]

3. **Additional point**: Set \( x = 1 \):
\[
y = -3(1) + 4 = 1 \quad \text{(Point: (1, 1))}
\]

### Equation 2: \( y = 3x - 2 \)

1. **Y-intercept**: Set \( x = 0 \):
\[
y = 3(0) - 2 = -2 \quad \text{(Point: (0, -2))}
\]

2. **X-intercept**: Set \( y = 0 \):
\[
0 = 3x - 2 \quad \Rightarrow \quad 3x = 2 \quad \Rightarrow \quad x = \frac{2}{3} \quad \text{(Point: (2/3, 0))}
\]

3. **Additional point**: Set \( x = 1 \):
\[
y = 3(1) - 2 = 1 \quad \text{(Point: (1, 1))}
\]

### Plotting the Lines

1. **Plot the points**:
- For \( y = -3x + 4 \): Plot (0, 4), (4/3, 0), and (1, 1).
- For \( y = 3x - 2 \): Plot (0, -2), (2/3, 0), and (1, 1).

2. **Draw the lines**: Connect the points for each line to create straight lines.

### Finding the Intersection

Both lines have the point (1, 1) in common. Hence, they intersect at that point.

### Graph Summary
- The line \( y = -3x + 4 \) has a negative slope and crosses the y-axis at (0, 4).
- The line \( y = 3x - 2 \) has a positive slope and crosses the y-axis at (0, -2).
- They intersect at (1, 1).

If you plot this on a coordinate grid, you'll have two lines that cross at point (1, 1).