has an x intercept of -7 and a slope of -2/3

If a line has an x-intercept of \(-7\) and a slope of \(-\frac{2}{3}\), we can write the equation of the line in slope-intercept form, \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

First, we know:
- The slope \(m = -\frac{2}{3}\).
- The x-intercept tells us the point \((-7, 0)\) lies on the line.

To find the y-intercept \(b\), substitute the x-intercept point \((-7, 0)\) into the slope-intercept equation:

\[
y = mx + b
\]
Substitute \(x = -7\), \(y = 0\), and \(m = -\frac{2}{3}\):

\[
0 = -\frac{2}{3}(-7) + b
\]

Now, solve for \(b\):

\[
0 = \frac{14}{3} + b
\]

\[
b = -\frac{14}{3}
\]

Thus, the equation of the line is:

\[
y = -\frac{2}{3}x - \frac{14}{3}
\]

Would you like more details or clarifications? Here are five related questions to explore further:

1. How do you find the slope given two points on a line?
2. What is the significance of the y-intercept in a graph?
3. How can you convert this equation to standard form?
4. What would be the effect of changing the slope on the graph?
5. How do parallel and perpendicular lines relate to their slopes?

**Tip:** The x-intercept is where the line crosses the x-axis, meaning \(y = 0\) at that point. This information is useful for solving equations.

Learn how to find the equation of a line given an x-intercept of -7 and a slope of -2/3. This step-by-step solution explains key concepts such as slope-intercept form (y = mx + b) and the process of calculating the y-intercept. Suitable for students in Grades 8-10.

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