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, $y = 0$.