To find the x-intercept and y-intercept of the given line:

$-8x + 5y = 14$

We need to follow these steps:

1. Finding the x-intercept:

The x-intercept occurs when $y = 0$. Substitute $y = 0$ into the equation:

$-8x + 5(0) = 14 \implies -8x = 14$

Solving for $x$:

$x = \frac{14}{-8} = -\frac{7}{4}$

So, the x-intercept is $x = -\frac{7}{4}$.

2. Finding the y-intercept:

The y-intercept occurs when $x = 0$. Substitute $x = 0$ into the equation:

$-8(0) + 5y = 14 \implies 5y = 14$

Solving for $y$:

$y = \frac{14}{5}$

So, the y-intercept is $y = \frac{14}{5}$.

Final Answer:

• The x-intercept is $-\frac{7}{4}$.
• The y-intercept is $\frac{14}{5}$.

Do you have any questions or would you like more details on how this was solved?

Here are some related questions to expand on this topic:

1. How do we graph a line using intercepts?
2. What is the slope of the line given by the equation $-8x + 5y = 14$?
3. How do you rewrite the equation in slope-intercept form?
4. What are the steps to find intercepts for quadratic equations?
5. How do the intercepts help in understanding the behavior of a linear function?

Tip: The x-intercept occurs where the graph crosses the x-axis, and the y-intercept occurs where the graph crosses the y-axis.