Determine the x-intercept of a straight line with a gradient of - 2 over 3 and y-intercept of 4

To find the x-intercept of a straight line, we use the slope-intercept form of the equation of a line:

\[
y = mx + c
\]

where:
- \( m \) is the slope (or gradient),
- \( c \) is the y-intercept.

Given:
- Slope \( m = -\frac{2}{3} \),
- Y-intercept \( c = 4 \).

The x-intercept occurs where \( y = 0 \). Substituting \( y = 0 \) into the equation:

\[
0 = -\frac{2}{3}x + 4
\]

Now solve for \( x \):

\[
\frac{2}{3}x = 4
\]

Multiply both sides by \( \frac{3}{2} \) to isolate \( x \):

\[
x = 4 \times \frac{3}{2} = 6
\]

Thus, the x-intercept is \( x = 6 \).

### Summary:
The x-intercept of the line is \( 6 \).

Would you like more details or have any questions? Here are some related questions:

1. What is the y-intercept of a line with a different slope, say 5, and passes through the origin?
2. How do you find the slope of a line given two points?
3. What is the general form of a line equation and how do you convert between forms?
4. If the line passes through the point (3, -2), how does the equation change?
5. How do parallel and perpendicular lines relate in terms of slope?

**Tip**: The x-intercept is where the line crosses the x-axis, meaning \( y = 0 \).

Learn how to find the x-intercept of a line with a gradient of -2/3 and a y-intercept of 4. This detailed step-by-step solution uses the slope-intercept formula to solve for x where y = 0, making it a great problem for students in Grades 7-9.

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