Let's solve each equation to find the x-intercepts and y-intercepts.

37. $x - y = 5$

• x-intercept: Set $y = 0$. $x - 0 = 5 \quad \Rightarrow \quad x = 5$ So, the x-intercept is $(5, 0)$.

• y-intercept: Set $x = 0$. $0 - y = 5 \quad \Rightarrow \quad y = -5$ So, the y-intercept is $(0, -5)$.

38. $x - y = -4$

• x-intercept: Set $y = 0$. $x - 0 = -4 \quad \Rightarrow \quad x = -4$ So, the x-intercept is $(-4, 0)$.

• y-intercept: Set $x = 0$. $0 - y = -4 \quad \Rightarrow \quad y = 4$ So, the y-intercept is $(0, 4)$.

39. $3x + y = 6$

• x-intercept: Set $y = 0$. $3x + 0 = 6 \quad \Rightarrow \quad x = 2$ So, the x-intercept is $(2, 0)$.

• y-intercept: Set $x = 0$. $3(0) + y = 6 \quad \Rightarrow \quad y = 6$ So, the y-intercept is $(0, 6)$.

40. $x - 2y = 8$

• x-intercept: Set $y = 0$. $x - 2(0) = 8 \quad \Rightarrow \quad x = 8$ So, the x-intercept is $(8, 0)$.

• y-intercept: Set $x = 0$. $0 - 2y = 8 \quad \Rightarrow \quad y = -4$ So, the y-intercept is $(0, -4)$.

41. $4x - y = 8$

• x-intercept: Set $y = 0$. $4x - 0 = 8 \quad \Rightarrow \quad x = 2$ So, the x-intercept is $(2, 0)$.

• y-intercept: Set $x = 0$. $4(0) - y = 8 \quad \Rightarrow \quad y = -8$ So, the y-intercept is $(0, -8)$.

42. $5x - y = 5$

• x-intercept: Set $y = 0$. $5x - 0 = 5 \quad \Rightarrow \quad x = 1$ So, the x-intercept is $(1, 0)$.

• y-intercept: Set $x = 0$. $5(0) - y = 5 \quad \Rightarrow \quad y = -5$ So, the y-intercept is $(0, -5)$.

43. $2x + 5y = 10$

• x-intercept: Set $y = 0$. $2x + 5(0) = 10 \quad \Rightarrow \quad x = 5$ So, the x-intercept is $(5, 0)$.

• y-intercept: Set $x = 0$. $2(0) + 5y = 10 \quad \Rightarrow \quad y = 2$ So, the y-intercept is $(0, 2)$.

44. $3x - 2y = 12$

• x-intercept: Set $y = 0$. $3x - 2(0) = 12 \quad \Rightarrow \quad x = 4$ So, the x-intercept is $(4, 0)$.

• y-intercept: Set $x = 0$. $3(0) - 2y = 12 \quad \Rightarrow \quad y = -6$ So, the y-intercept is $(0, -6)$.

Would you like any more details on these solutions or have further questions?

Follow-up questions:

1. How do you find the slope of a linear equation from intercepts?
2. How do x- and y-intercepts help in graphing a line?
3. What is the general form of a linear equation, and how do you convert it to slope-intercept form?
4. Can you use the intercepts to check the accuracy of the solution graphically?
5. What happens when an equation has no x-intercept or no y-intercept?

Tip: Always double-check your intercepts by substituting them back into the original equation to verify!