To help you with this exercise, I’ll analyze the graph to determine the $x$-intercepts and $y$-intercepts for the provided questions. Let’s break it down step-by-step:

Part i: State the value of the $x$-intercept

The $x$-intercept occurs where the line crosses the $x$-axis ($y = 0$).

a) The line crosses the $x$-axis at $(-2, 0)$.

Answer: $x$-intercept = $-2$.

b) The line crosses the $x$-axis at $(2, 0)$.

Answer: $x$-intercept = $2$.

c) The line crosses the $x$-axis at approximately $(-1.5, 0)$.

Answer: $x$-intercept = $-1.5$.

d) The line crosses the $x$-axis at $(4, 0)$.

Answer: $x$-intercept = $4$.

Part ii: State the value of the $y$-intercept

The $y$-intercept occurs where the line crosses the $y$-axis ($x = 0$).

a) The line crosses the $y$-axis at $(0, 2)$.

Answer: $y$-intercept = $2$.

b) The line crosses the $y$-axis at $(0, 4)$.

Answer: $y$-intercept = $4$.

c) The line crosses the $y$-axis at approximately $(0, 2.5)$.

Answer: $y$-intercept = $2.5$.

d) The line crosses the $y$-axis at $(0, -1)$.

Answer: $y$-intercept = $-1$.

Would you like me to explain how intercepts are calculated in more detail or analyze anything else? 😊

5 Related Questions:

1. What do $x$- and $y$-intercepts tell us about the graph of a function?
2. How can you find intercepts algebraically from an equation?
3. Can a line have more than one $x$- or $y$-intercept? Why or why not?
4. How are intercepts useful in solving real-world problems involving graphs?
5. What are the differences between intercepts in linear versus non-linear graphs?

Tip: Always verify the intercepts by substituting into the equation of the line, if available.