To graph the line represented by the equation $2x - 5y = 10$ by finding and plotting the intercepts, let's proceed as follows:

Step 1: Find the x-intercept

The x-intercept occurs when $y = 0$.

1. Substitute $y = 0$ in the equation: $2x - 5(0) = 10 \Rightarrow 2x = 10 \Rightarrow x = 5$
2. So, the x-intercept is at $(5, 0)$.

Step 2: Find the y-intercept

The y-intercept occurs when $x = 0$.

1. Substitute $x = 0$ in the equation: $2(0) - 5y = 10 \Rightarrow -5y = 10 \Rightarrow y = -2$
2. So, the y-intercept is at $(0, -2)$.

Step 3: Plot the points and draw the line

1. Plot the points $(5, 0)$ and $(0, -2)$ on the graph.
2. Draw a straight line through these two points to represent the equation.

Would you like further details on graphing or have any other questions?

Here are 5 related questions to further explore this topic:

1. How can we rewrite the equation $2x - 5y = 10$ in slope-intercept form?
2. How do you determine the slope of the line from its standard form equation?
3. What are some other ways to graph a line without finding intercepts?
4. How does changing the coefficients in $2x - 5y = 10$ affect the line's graph?
5. What does it mean if two lines have the same slope but different y-intercepts?

Tip: To find intercepts quickly, set one variable to zero and solve for the other variable.