https://file.aiquickdraw.com/mathbot/file/17272284608968wujh1d5.jpg

Let's solve the given equation to find the x- and y-intercepts.

The equation provided is:
\[
-7y - 3x = -21
\]

### Finding the x-intercept:
To find the x-intercept, set \(y = 0\) and solve for \(x\):

\[
-7(0) - 3x = -21
\]
\[
-3x = -21
\]
\[
x = \frac{-21}{-3} = 7
\]

So, the x-intercept is \(x = 7\).

### Finding the y-intercept:
To find the y-intercept, set \(x = 0\) and solve for \(y\):

\[
-7y - 3(0) = -21
\]
\[
-7y = -21
\]
\[
y = \frac{-21}{-7} = 3
\]

So, the y-intercept is \(y = 3\).

Thus, the correct intercepts are:
- x-intercept: \(7\)
- y-intercept: \(3\)

The values entered in the image are slightly incorrect because they include an extra "0," and should just be:
- x-intercept: 7
- y-intercept: 3

Would you like any further details or explanations?

Here are 5 related questions to extend this problem:
1. How do you graph the line based on the x- and y-intercepts?
2. What is the slope of the line given by the equation \( -7y - 3x = -21 \)?
3. How can you rewrite the equation in slope-intercept form?
4. What would happen to the intercepts if the equation were multiplied by a constant?
5. How can you determine the equation of a line given the intercepts?

**Tip:** Remember, for any linear equation, the intercepts are found by setting one variable to zero and solving for the other.

Find the x and y intercepts of the following equation: -7y - 3x = -21

Learn how to find the x and y intercepts of the linear equation -7y - 3x = -21. This step-by-step solution covers key algebraic concepts and is suitable for students in Grades 8-10.

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