Let's go through each problem one by one. Here’s how to approach the first set:

39. Write an equation of the line in slope-intercept form.

• Slope: $\frac{1}{2}$
• Point: $(6, -2)$

Slope-intercept form: $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

• Using the given slope $m = \frac{1}{2}$ and the point $(6, -2)$, we can substitute into the equation to find $b$.

The equation is: $y - (-2) = \frac{1}{2}(x - 6)$ Simplifying this equation will give us the slope-intercept form.

40. Write an equation of the line in slope-intercept form.

• Points: $(2, 1)$, $(6, -1)$

To find the slope, use the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substitute the points into this formula to find the slope, then plug into the slope-intercept form to find the full equation.

41. Write an equation of the line in point-slope form.

• Points: $(1, 3)$, $(6, 5)$

Use the point-slope form equation: $y - y_1 = m(x - x_1)$ where $m$ is the slope (calculated similarly to above) and $(x_1, y_1)$ is a point on the line.

Would you like to continue solving these problems step by step or would you prefer a more detailed explanation of any of them? Let me know how you'd like to proceed!

Related Questions:

1. How do you derive the slope-intercept form of a line from a point and slope?
2. How do you find the slope of a line from two points?
3. What is the difference between slope-intercept and point-slope form?
4. How do parallel and perpendicular lines relate to their slopes?
5. How do you solve a system of linear equations using substitution or elimination?

Tip:

When working with point-slope and slope-intercept forms, remember to always carefully check your points and slopes to ensure you are calculating the equation accurately!