To find the x- and y-intercepts of the equation $5x + 2y = 20$, we’ll solve for each intercept separately:

1. Finding the x-intercept:

For the x-intercept, set $y = 0$ and solve for $x$. $5x + 2(0) = 20$ $5x = 20$ $x = \frac{20}{5} = 4$ So, the x-intercept is $x = 4$.

2. Finding the y-intercept:

For the y-intercept, set $x = 0$ and solve for $y$. $5(0) + 2y = 20$ $2y = 20$ $y = \frac{20}{2} = 10$ So, the y-intercept is $y = 10$.

Final Answer:

• x-intercept: 4
• y-intercept: 10

Would you like additional details on the solution, or have any questions about it?

Here are some related questions to explore this topic further:

1. What would the intercepts be if the equation was $5x + 2y = 15$?
2. How would you find intercepts if the equation involved a fraction, such as $\frac{5}{2}x + y = 20$?
3. How does changing the slope of the line affect the x- and y-intercepts?
4. Can you determine intercepts if the line equation is given in slope-intercept form, like $y = mx + b$?
5. How do x- and y-intercepts help in graphing a linear equation?

Tip: Setting $y = 0$ finds the x-intercept, while setting $x = 0$ finds the y-intercept. This is a quick way to check key points on a line.