The uploaded image contains a math worksheet asking students to write equations of lines in slope-intercept form. It includes two parts:

1. Given the slope and y-intercept:
   Students are asked to write equations of lines using the provided slope $m$ and y-intercept $b$.

2. Using a graph:
   Students are tasked to calculate the slope by determining the "rise" (change in $y$) and "run" (change in $x$) from a graph. The slope is used alongside the $y$-intercept to form the equation.

Explanation and Steps for Solving:

1. Slope-intercept form:
   The equation of a line is $y = mx + b$, where:

   • $m$: slope of the line.
   • $b$: $y$-intercept (the point where the line crosses the $y$-axis).

2. Using given values of slope and y-intercept: Example from the image:

   • For slope $m = -2$ and $y$-intercept $b = 5$, the equation is:
     $y = -2x + 5$

3. Finding slope from a graph:

   • Select two points on the line (e.g., (3,1) and (1,-5) from the graph).

   • Calculate the rise (difference in $y$-values) and run (difference in $x$-values):
     $\text{slope } m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}$

   • For the example graph: $\text{rise } = 1 - (-5) = 6, \, \text{run } = 3 - 1 = 2$ $m = \frac{6}{2} = 3$

4. Write the equation: Use the calculated slope and $y$-intercept (from the graph, $b = 1$):
   $y = 3x + 1$

Would you like me to solve the specific equations or provide explanations for any part?

Here are some related questions:

1. How do you find the slope if only two points are given?
2. What are the steps to graph a line given its equation in slope-intercept form?
3. How can you identify the $y$-intercept directly from a graph?
4. Can you explain how slope triangles work for calculating slope?
5. How do vertical and horizontal lines differ in terms of slope?

Tip: Always double-check rise and run directions (up/down or left/right) to ensure the slope is calculated correctly!