Find the x- and y-intercepts of the graph of 8, x, plus, 2, y, equals, 348x+2y=34. State each answer as an integer or an improper fraction in simplest form.

The equation provided is:

\[
8x + 2y = 34
\]

To find the intercepts, we'll evaluate the equation for both \(x\)-intercepts and \(y\)-intercepts separately.

### 1. **Finding the \(x\)-intercept**:
For the \(x\)-intercept, set \(y = 0\) in the equation and solve for \(x\):

\[
8x + 2(0) = 34
\]
\[
8x = 34
\]
\[
x = \frac{34}{8} = \frac{17}{4}
\]

Thus, the \(x\)-intercept is \(x = \frac{17}{4}\), and the coordinate point is:
\[
\left(\frac{17}{4}, 0\right)
\]

### 2. **Finding the \(y\)-intercept**:
For the \(y\)-intercept, set \(x = 0\) in the equation and solve for \(y\):

\[
8(0) + 2y = 34
\]
\[
2y = 34
\]
\[
y = \frac{34}{2} = 17
\]

Thus, the \(y\)-intercept is \(y = 17\), and the coordinate point is:
\[
(0, 17)
\]

### Summary:
- The \(x\)-intercept is \(\left(\frac{17}{4}, 0\right)\).
- The \(y\)-intercept is \((0, 17)\).

Would you like more details or have any questions? 

Here are 5 related questions to expand this concept:
1. How do you convert an improper fraction into a mixed number?
2. What is the general form of a linear equation, and how does it help find intercepts?
3. Can a linear equation have more than one \(x\)- or \(y\)-intercept?
4. What happens to the intercepts if you change the coefficients in the equation?
5. How can you graph this equation using the intercepts?

**Tip**: The intercepts of a line provide quick and easy points to plot when graphing the equation!

Find the x- and y-intercepts of the graph of 8x + 2y = 34. State each answer as an integer or an improper fraction in simplest form.

Learn how to find the x- and y-intercepts of the linear equation 8x + 2y = 34. This guide provides a step-by-step solution using algebraic concepts and formulas, suitable for students in Grades 8-10. Understand how to simplify fractions and calculate intercepts easily.

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