Find the y-intercept and x-intercept of the following linear equation.

−7x+6y=−9

To find the intercepts of the linear equation \( -7x + 6y = -9 \), let's analyze each type of intercept separately.

### 1. **Finding the y-intercept:**
The y-intercept is the point where the line crosses the y-axis. At this point, \( x = 0 \).

Substitute \( x = 0 \) into the equation:
\[
-7(0) + 6y = -9
\]
This simplifies to:
\[
6y = -9
\]
Now, divide both sides by 6:
\[
y = -\frac{9}{6} = -\frac{3}{2}
\]

So, the **y-intercept** is \( \left(0, -\frac{3}{2}\right) \).

### 2. **Finding the x-intercept:**
The x-intercept is the point where the line crosses the x-axis. At this point, \( y = 0 \).

Substitute \( y = 0 \) into the equation:
\[
-7x + 6(0) = -9
\]
This simplifies to:
\[
-7x = -9
\]
Now, divide both sides by -7:
\[
x = \frac{9}{7}
\]

So, the **x-intercept** is \( \left(\frac{9}{7}, 0\right) \).

### Summary
- **y-intercept**: \( \left(0, -\frac{3}{2}\right) \)
- **x-intercept**: \( \left(\frac{9}{7}, 0\right) \)

Would you like further details on intercepts, or have any questions?

Here are some additional questions for practice:
1. How would you find the intercepts of the equation \( 5x - 3y = 15 \)?
2. If a line has an x-intercept of 4 and a y-intercept of -2, what is its equation in slope-intercept form?
3. What is the x-intercept of the equation \( 2x + y = 10 \)?
4. How can you verify the intercepts of the equation \( 3x - 6y = 12 \)?
5. For a given line, how does changing the slope affect the intercepts?

**Tip:** When finding intercepts, always remember that at the y-intercept, \( x = 0 \) and at the x-intercept, \( y = 0 \).

Find the y-intercept and x-intercept of the following linear equation: −7x+6y=−9

Discover how to find the x-intercept and y-intercept of the linear equation −7x + 6y = −9 through a clear, step-by-step solution. This problem explores key algebraic concepts and is suitable for students in Grades 7-9.

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