Find the x- and y-intercepts of the graph of x, minus, 3, y, equals, 7x−3y=7. State each answer as an integer or an improper fraction in simplest form.

To find the x- and y-intercepts of the equation \( 7x - 3y = 7 \), we follow these steps:

### 1. Finding the x-intercept:
The x-intercept occurs when \( y = 0 \). So, substitute \( y = 0 \) into the equation:

\[
7x - 3(0) = 7
\]

\[
7x = 7
\]

\[
x = \frac{7}{7} = 1
\]

Thus, the x-intercept is \( (1, 0) \).

### 2. Finding the y-intercept:
The y-intercept occurs when \( x = 0 \). So, substitute \( x = 0 \) into the equation:

\[
7(0) - 3y = 7
\]

\[
-3y = 7
\]

\[
y = \frac{7}{-3} = -\frac{7}{3}
\]

Thus, the y-intercept is \( \left(0, -\frac{7}{3}\right) \).

### Final Answer:
- The x-intercept is \( (1, 0) \)
- The y-intercept is \( \left(0, -\frac{7}{3}\right) \)

Would you like more details or have any questions?

Here are 5 related questions for practice:
1. Find the x- and y-intercepts of \( 4x - 5y = 20 \).
2. What is the slope of the line \( 7x - 3y = 7 \)?
3. Determine the x- and y-intercepts of \( 2x + 6y = 12 \).
4. Solve for the intercepts of \( 5x - 7y = -14 \).
5. What are the intercepts of \( 3x + 4y = 12 \)?

**Tip:** To find the intercepts quickly, always substitute zero for the other variable!

Find the x- and y-intercepts of the graph of 7x - 3y = 7. State each answer as an integer or an improper fraction in simplest form.

This problem demonstrates how to find the x- and y-intercepts of the linear equation 7x - 3y = 7. Learn how to substitute variables to calculate intercepts, essential for understanding linear equations. Suitable for students in Grades 8-10.

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