Question

What is the 'intercept of the line given by the equation below?
y= 4x - 6
• A. (0,4)
• в. (-6, 0)
• c. (4,0)
• D. (0, -6)

Answer 1

To find the intercept of the line given by the equation \( y = 4x - 6 \), we can find both the y-intercept and the x-intercept.

1. **Y-intercept**: This is the point where the line crosses the y-axis (where \( x = 0 \)).
- Substitute \( x = 0 \) into the equation:
\[
y = 4(0) - 6 = -6
\]
- So, the y-intercept is \( (0, -6) \).

2. **X-intercept**: This is the point where the line crosses the x-axis (where \( y = 0 \)).
- Set \( y = 0 \) in the equation:
\[
0 = 4x - 6
\]
- Solve for \( x \):
\[
4x = 6 \implies x = \frac{6}{4} = \frac{3}{2}
\]
- So, the x-intercept is \( \left(\frac{3}{2}, 0\right) \).

Based on the options you provided, the y-intercept of the line is:

**D. (0, -6)**.