To solve the given problem, we need to find the x-intercept and y-intercept of the line represented by the equation:

$-5x + 6y = 9$

Step 1: Find the y-intercept

The y-intercept occurs when $x = 0$. Substituting $x = 0$ into the equation:

$-5(0) + 6y = 9$ $6y = 9$ $y = \frac{9}{6} = \frac{3}{2}$

So, the y-intercept is $\frac{3}{2}$.

Step 2: Find the x-intercept

The x-intercept occurs when $y = 0$. Substituting $y = 0$ into the equation:

$-5x + 6(0) = 9$ $-5x = 9$ $x = \frac{9}{-5} = -\frac{9}{5}$

So, the x-intercept is $-\frac{9}{5}$.

Final Answer:

• y-intercept: $\frac{3}{2}$
• x-intercept: $-\frac{9}{5}$

Would you like further details or have any additional questions?

Here are 5 related questions for practice:

1. How do you find the slope of the line $-5x + 6y = 9$?
2. What is the slope-intercept form of the line $-5x + 6y = 9$?
3. If the equation were $5x - 6y = -9$, what would the intercepts be?
4. How do you graph the line using the intercepts $\frac{3}{2}$ and $-\frac{9}{5}$?
5. What is the distance from the origin to the y-intercept of this line?

Tip: Always substitute $x = 0$ for the y-intercept and $y = 0$ for the x-intercept directly into the equation!