A line passes through the point (0,12) and has a slope of 2/3 What is the x
-intercept of the line? (___________,__________)

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

\[
y = mx + b
\]

where:
- \( m = \frac{2}{3} \) is the slope,
- \( b = 12 \) is the y-intercept, as the point (0, 12) is given.

The x-intercept occurs when \( y = 0 \). Plug this into the equation to solve for \( x \):

\[
0 = \frac{2}{3}x + 12
\]

Now solve for \( x \):

\[
\frac{2}{3}x = -12
\]

\[
x = \frac{-12 \times 3}{2} = -18
\]

Thus, the x-intercept is at the point \( (-18, 0) \).

Would you like more details or have any questions about this solution?

Here are 5 related questions to expand on this:
1. How would you find the y-intercept if it wasn’t already given?
2. What is the slope-intercept form of a line, and why is it useful?
3. How do you find the equation of a line that passes through two given points?
4. What is the general form of a linear equation, and how can you convert between forms?
5. Can a line have both positive and negative intercepts? Why?

**Tip:** Always remember that the x-intercept occurs when \( y = 0 \) and the y-intercept occurs when \( x = 0 \).

A line passes through the point (0,12) and has a slope of 2/3. What is the x-intercept of the line? (___________,__________)

Discover how to find the x-intercept of a line that passes through (0,12) with a slope of 2/3 using the point-slope form equation. This problem covers algebraic concepts suitable for Grades 8-10 students, helping to understand linear equations and intercepts.

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