To solve this "Equation of a line matching activity," we need to match each point and slope with its corresponding equation. Here's how to approach each one:

Approach:

1. Identify the form of each line equation: Most equations given are in the slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
2. Check each option: Either by calculating the slope from two points provided or by identifying the slope and a point that lies on each line equation.

Solution Steps:

I'll go through each problem systematically. Here is the breakdown of a few examples to get started.

Example Matching:

1. 1. $m = -3$; (-4, 1):

   • Equation with slope $m = -3$ and point (-4, 1).
   • Check equation options with $m = -3$, such as $y = -3x + 4$.

2. 2. $(4, -8)$ and $(-20, 10)$:

   • Calculate slope $m = \frac{-8 - 10}{4 + 20} = -\frac{3}{4}$.
   • Check equation options with slope $-\frac{3}{4}$, such as $y = -\frac{3}{4}x + 9$.

Would you like me to continue solving each one systematically?

Possible Follow-up Questions:

1. How do you calculate the slope between two points?
2. What if a point doesn’t satisfy an equation—does that mean it’s not a solution?
3. Can slope-intercept form be converted to standard form and vice versa?
4. Are there cases where two points determine more than one equation?
5. What are the methods for quickly identifying the y-intercept?

Tip:

When given two points, use the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$ to find the slope, which can guide you in identifying the correct line equation.