The worksheet asks to write equations in point-slope form for lines passing through two given points. The point-slope form equation is:

$y - y_1 = m(x - x_1)$

where $m$ is the slope, and $(x_1, y_1)$ is a point on the line. The slope $m$ can be found using the formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

I'll help you solve each question by finding the slope and using one of the points in the equation.

1. Through: (-3, 4) and (-4, -5)

• Slope: $m = \frac{-5 - 4}{-4 - (-3)} = \frac{-9}{-1} = 9$ Using point (-3, 4): $y - 4 = 9(x + 3)$

2. Through: (-3, -2) and (0, -4)

• Slope: $m = \frac{-4 - (-2)}{0 - (-3)} = \frac{-2}{3}$ Using point (-3, -2): $y + 2 = -\frac{2}{3}(x + 3)$

3. Through: (0, -5) and (2, 3)

• Slope: $m = \frac{3 - (-5)}{2 - 0} = \frac{8}{2} = 4$ Using point (0, -5): $y + 5 = 4(x - 0)$

4. Through: (-3, 2) and (4, 4)

• Slope: $m = \frac{4 - 2}{4 - (-3)} = \frac{2}{7}$ Using point (-3, 2): $y - 2 = \frac{2}{7}(x + 3)$

5. Through: (-4, -5) and (-5, -3)

• Slope: $m = \frac{-3 - (-5)}{-5 - (-4)} = \frac{2}{-1} = -2$ Using point (-4, -5): $y + 5 = -2(x + 4)$

Would you like more details on any of the solutions? Here are five related questions for further practice:

1. What is the equation of a line through (1, 2) and (3, 8) in point-slope form?
2. How do you convert point-slope form to slope-intercept form?
3. Can you write the equation for a vertical line through the points (2, 4) and (2, -3)?
4. What is the slope of a line parallel to $y = 3x + 7$?
5. How do you find the midpoint between two points?

Tip: Always check the slope calculation carefully—this determines the accuracy of your final equation!