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!