https://file.aiquickdraw.com/mathbot/file/1729102476095qw6ireif.jpg

Let's analyze the problem step-by-step. The given equation is:

\[
10x + 7y = 35
\]

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

\[
10x + 7(0) = 35 \quad \Rightarrow \quad 10x = 35 \quad \Rightarrow \quad x = \frac{35}{10} = 3.5
\]

So, the x-intercept is \( x = 3.5 \).

The correct answer to the multiple-choice question would be **A**, with the x-intercept being **3.5**.

### b) Use the x- and y-intercepts to sketch the graph:
You can now use the intercepts to graph the line:

- X-intercept: \( (3.5, 0) \)
- Y-intercept: To find the y-intercept, set \( x = 0 \) and solve for \( y \):

\[
10(0) + 7y = 35 \quad \Rightarrow \quad 7y = 35 \quad \Rightarrow \quad y = \frac{35}{7} = 5
\]

Thus, the y-intercept is \( y = 5 \) or \( (0, 5) \).

These points can be plotted on a coordinate plane to sketch the line.

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Would you like further details or help with another part of this problem?

Here are 5 related questions to explore further:
1. How do you find the slope of the line from its intercepts?
2. What is the general formula for finding intercepts of a linear equation?
3. How can you verify your intercepts using substitution?
4. Can you find the intercepts of a vertical or horizontal line?
5. What is the significance of intercepts in real-life problems?

**Tip**: When finding intercepts, always set the opposite variable to zero and solve for the remaining one!

Determine the x- and y-intercepts of the line 10x + 7y = 35, and use them to sketch the graph of the line.

Learn how to determine the x- and y-intercepts of the linear equation 10x + 7y = 35 and how to use them to sketch the graph of the line. This problem covers key concepts in algebra, including solving for intercepts and graphing lines. Suitable for students in Grades 8-10.

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