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

$10x + 8y = 20$

Finding the x-intercept:

The x-intercept occurs when $y = 0$. So, substitute $y = 0$ into the equation:

$10x + 8(0) = 20$ $10x = 20$ $x = \frac{20}{10} = 2$

Thus, the x-intercept is $x = 2$.

Finding the y-intercept:

The y-intercept occurs when $x = 0$. So, substitute $x = 0$ into the equation:

$10(0) + 8y = 20$ $8y = 20$ $y = \frac{20}{8} = \frac{5}{2}$

Thus, the y-intercept is $y = \frac{5}{2}$.

Final Answers:

• x-intercept: $x = 2$
• y-intercept: $y = \frac{5}{2}$

Would you like more details or have any questions? Here are some related questions for further exploration:

1. How can you use the slope-intercept form of a line to find intercepts?
2. What does the slope of a line represent in terms of intercepts?
3. How do you find intercepts for other linear equations in standard form?
4. Can you identify the intercepts of a vertical or horizontal line?
5. How can you graph a line once you have its intercepts?

Tip: When finding intercepts, set the opposite variable to zero and solve for the remaining variable.