https://file.aiquickdraw.com/mathbot/file/1725497898785y4358s1p.jpg

The equation provided in the image is:

\[
5x - 2y = -10
\]

To graph this line using intercepts, we will find the **x-intercept** and the **y-intercept**.

### Step 1: Find the x-intercept
To find the x-intercept, set \( y = 0 \) and solve for \( x \):

\[
5x - 2(0) = -10 \implies 5x = -10 \implies x = -2
\]

So, the x-intercept is \( (-2, 0) \).

### Step 2: Find the y-intercept
To find the y-intercept, set \( x = 0 \) and solve for \( y \):

\[
5(0) - 2y = -10 \implies -2y = -10 \implies y = 5
\]

So, the y-intercept is \( (0, 5) \).

### Step 3: Plot the intercepts and draw the line
- Plot the point \( (-2, 0) \) on the x-axis.
- Plot the point \( (0, 5) \) on the y-axis.
- Draw a straight line through these two points to graph the equation.

Would you like a detailed drawing of the graph? Also, here are some questions to extend your understanding:

1. What happens if we multiply both sides of the equation by a constant?
2. How do you determine the slope from the equation \( 5x - 2y = -10 \)?
3. What is the slope of the line from the two intercepts?
4. Can you write this equation in slope-intercept form?
5. How would you graph the line if given only the slope and a point?

**Tip:** Always check for both intercepts (x and y) to quickly graph a linear equation!

Graph the line 5x - 2y = -10 using intercepts.

Learn how to graph the linear equation 5x - 2y = -10 using x and y intercepts. This problem demonstrates key algebraic concepts like finding intercepts and graphing linear equations step-by-step. Suitable for students in Grades 8-10.

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