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!