Let's walk through the answers for the slope-intercept form questions on the worksheet.

1. First Graph:

The slope-intercept form is given by the equation: $y = mx + b$ Where:

• $m$ is the slope.
• $b$ is the y-intercept.

From the graph:

• The slope ($m$) is the change in $y$ divided by the change in $x$ between two points on the line. Let's take two points from the graph: (0, 3) and (2, 0).

  • From (0, 3) to (2, 0), the change in $y$ is $0 - 3 = -3$, and the change in $x$ is $2 - 0 = 2$.
  • So, the slope $m = \frac{-3}{2} = -\frac{3}{2}$.

• The y-intercept ($b$) is the point where the line crosses the y-axis. From the graph, it crosses at $(0, 3)$, so $b = 3$.

• The x-intercept is the point where the line crosses the x-axis, which from the graph is $(2, 0)$.

Thus, the equation of the line is: $y = -\frac{3}{2}x + 3$

2. Table:

For each equation in the table, let's find the slope ($m$) and the y-intercept ($b$).

1. $y = 2x + 5$:

   • Slope ($m$) = 2
   • Y-intercept ($b$) = 5

2. $y = -x - 3$:

   • Slope ($m$) = -1 (since $-x$ is equivalent to $-1x$)
   • Y-intercept ($b$) = -3

3. $y = 7$:

   • This is a horizontal line where $y = 7$ for all $x$, so the slope ($m$) = 0.
   • Y-intercept ($b$) = 7

4. $y = -x$:

   • Slope ($m$) = -1
   • Y-intercept ($b$) = 0 (since no constant is added, $b = 0$)

Let me know if you'd like any further details or clarifications.

Follow-up questions:

1. How can you identify the slope from an equation in slope-intercept form?
2. What does the y-intercept tell you about a graph?
3. How do you determine the x-intercept from a graph?
4. What happens to the graph when the slope is positive versus negative?
5. Can you have a slope with a zero y-intercept? What would it look like?

Tip:

To find the slope from a graph, always pick two clear points on the line and use the formula $\text{slope} = \frac{\Delta y}{\Delta x}$.