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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?

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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.

Graph the line by finding and plotting the intercepts for the equation 2x - 5y = 10

Learn how to graph the line represented by the equation 2x - 5y = 10 by finding and plotting the x- and y-intercepts. This problem covers key algebra concepts, including linear equations and intercepts, suitable for students in Grades 8-10.

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