Let's analyze and sketch the graphs of the given linear relations by finding their x- and y-intercepts.

a) $2x - 5y = -10$

Step 1: Find the x-intercept.

• The x-intercept occurs when $y = 0$. $2x - 5(0) = -10 \implies 2x = -10 \implies x = -5$ So, the x-intercept is $(-5, 0)$.

Step 2: Find the y-intercept.

• The y-intercept occurs when $x = 0$. $2(0) - 5y = -10 \implies -5y = -10 \implies y = 2$ So, the y-intercept is $(0, 2)$.

Step 3: Sketch the graph.

• Plot the points $(-5, 0)$ and $(0, 2)$.
• Draw a straight line through these two points.

b) $y = -2x + 4$

This equation is already in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Step 1: Find the y-intercept.

• The y-intercept is $(0, 4)$.

Step 2: Find the x-intercept.

• The x-intercept occurs when $y = 0$. $0 = -2x + 4 \implies 2x = 4 \implies x = 2$ So, the x-intercept is $(2, 0)$.

Step 3: Sketch the graph.

• Plot the points $(0, 4)$ and $(2, 0)$.
• Draw a straight line through these two points.

Graphing Both Equations

Now that we have the intercepts, the graphs can be drawn on the same coordinate plane.

Would you like a visual representation of these graphs? If yes, I can create that for you.

---

Do you want any more details or have questions? Here are some related questions:

1. What is the slope of each line, and how can it be interpreted?
2. How do you determine if two lines are parallel or perpendicular?
3. What does it mean when two lines have the same y-intercept?
4. How do you find the point of intersection between two lines?
5. Can you write an equation of a line parallel to $2x - 5y = -10$?

Tip: Always double-check the intercepts to ensure accuracy when sketching linear graphs.