Question

(3, 2)
Match the equation with the line from the system shown on the graph.
Purple Line ____________
Blue Line _____________
Options: y = 3x - 4, y = 2/3x, y = -1/2 x, y = -3/2x - 4, y = 3/2x, y = 2x - 4

Answer 1

To match the equations with the lines shown in the graph, we need to first analyze the characteristics of each line (slope and y-intercept) and compare them with the given equations.

1. **Purple Line:**
- Check the slope and y-intercept of the purple line.
- If the line rises steeply and intersects the y-axis at a negative value, the equation could be one with a positive slope, like \( y = \frac{3}{2}x \) or \( y = 3x - 4 \). A lower slope might suggest something like \( y = \frac{2}{3}x \) or \( y = -\frac{1}{2}x \), etc.
- Without a visual, let's assume we deduce its properties match \( y = 3x - 4 \) (for a steep line that cuts below y-axis) or could be \( y = \frac{3}{2}x\) as a moderate incline.

2. **Blue Line:**
- Similarly, for the blue line, observe if it's more horizontal or vertical, the slope, and its y-intercept.
- A negative slope might suggest an equation like \( y = -\frac{1}{2}x \) or \( y = -\frac{3}{2}x - 4 \).
- If it becomes consistent with a gentle descent, we might lean towards \( y = -\frac{1}{2}x \).

Assuming you do not have a visual reference here, you can proceed to check characteristics by substitution if you have specific points where these lines cross or intersect. Based on typical slope interpretation:

- If the **purple line** is steep and positively increasing, we can assign: **Purple Line = \( y = 3x - 4 \)**
- If the **blue line** has a more gradual or negative slope: **Blue Line = \( y = -\frac{1}{2}x \)**

So, I provide a general answer based on common transformations:

**Purple Line = \( y = 3x - 4 \)**
**Blue Line = \( y = -\frac{1}{2}x \)**

Adjust based on specific slope from your graph.