To solve each question, let's examine the graphs and determine the equations for each line.

Left Graph

1. The line has a positive slope, moving upwards as $x$ increases.

2. The line appears to pass through points with integer values, making it easier to calculate the slope. Let's use two points on the line:

   • Point 1: (0, -6)
   • Point 2: (4, -2)

3. Calculate the slope (m) using the formula: $m = \frac{{y_2 - y_1}}{{x_2 - x_1}} = \frac{{-2 - (-6)}}{{4 - 0}} = \frac{4}{4} = 1$

4. Since the line has a slope of 1 and passes through $y$-intercept $-6$, the equation is: $y = x - 6$

5. For the options:

   • Select "and add" for the rule, with $-6$ as the value to add.

Right Graph

1. This line also has a positive slope, passing through clear points.

2. Choose two points on the line:

   • Point 1: (0, -4)
   • Point 2: (4, 0)

3. Calculate the slope (m): $m = \frac{{y_2 - y_1}}{{x_2 - x_1}} = \frac{{0 - (-4)}}{{4 - 0}} = \frac{4}{4} = 1$

4. With a slope of 1 and $y$-intercept $-4$, the equation is: $y = x - 4$

5. For the options:

   • Choose "and add" with $-4$.

Summary

• Left Graph: Equation $y = x - 6$, rule "and add -6."
• Right Graph: Equation $y = x - 4$, rule "and add -4."

Would you like further details on slope calculation or equation formation?

1. What is the formula for calculating slope?
2. How can you determine the $y$-intercept from a graph?
3. What does a positive slope indicate about the direction of a line?
4. How can you verify an equation by substituting points?
5. What is the general form of a linear equation?

Tip: When finding the equation of a line, remember that the slope-intercept form $y = mx + b$ is useful if you can determine the slope $m$ and the $y$-intercept $b$ directly from the graph.