Let's solve the remaining problems, #17 and #18, using the same steps:

Problem 17

• Given: Point $(6, 2)$ and slope $\frac{2}{3}$
• Solution:
  1. Point-Slope Form: Use the formula $y - y_1 = m(x - x_1)$. $y - 2 = \frac{2}{3}(x - 6)$
  2. Distribute the slope: $y - 2 = \frac{2}{3}x - 4$
  3. Slope-Intercept Form: Solve for $y$ by adding 2 to both sides: $y = \frac{2}{3}x - 2$

Problem 18

• Given: Points $(2, -2)$ and $(4, -1)$
• Solution:
  1. Find the Slope $m$: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - (-2)}{4 - 2} = \frac{1}{2}$
  2. Point-Slope Form: Use $(2, -2)$ as the point and $m = \frac{1}{2}$: $y + 2 = \frac{1}{2}(x - 2)$
  3. Distribute the slope: $y + 2 = \frac{1}{2}x - 1$
  4. Slope-Intercept Form: Solve for $y$ by subtracting 2 from both sides: $y = \frac{1}{2}x - 3$

Would you like a more detailed explanation for any of these steps, or do you have any other questions?

Related Questions:

1. How do you derive the slope formula between two points?
2. What are the steps to convert from point-slope form to slope-intercept form?
3. Can the slope-intercept form always be derived from the point-slope form?
4. Why is it necessary to distribute the slope when using the point-slope form?
5. How would these equations change if the slope was negative?

Tip:

Remember, point-slope form is particularly useful for quickly setting up an equation when a single point and slope are known.