From the graph provided, we can determine the slope and point based on the labeled point and the line.

Point:

The labeled point on the graph is $(-2, 2)$.

Slope (m):

The slope $m$ is determined by the change in $y$ over the change in $x$ (rise over run).

• From the graph, if we move from the point $(-2, 2)$ to the next convenient point on the line, say $(0, 3)$:
  • Rise (change in $y$) = $3 - 2 = 1$
  • Run (change in $x$) = $0 - (-2) = 2$

So, the slope $m = \frac{1}{2}$.

Equation in Point-Slope Form:

The point-slope form of a line is given by:

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

Using the point $(-2, 2)$ and the slope $m = \frac{1}{2}$, we substitute into the equation:

$y - 2 = \frac{1}{2}(x + 2)$

Summary:

• Equation: $y - 2 = \frac{1}{2}(x + 2)$
• Slope: $\frac{1}{2}$
• Point: $(-2, 2)$

Would you like more details or further clarification on the process?

Here are five follow-up questions:

1. How do we convert this equation into slope-intercept form?
2. What is the y-intercept of this line?
3. Can we write the equation in standard form?
4. How do we find the x-intercept of this line?
5. What happens to the slope if the line becomes vertical?

Tip: When working with slopes, remember that a positive slope means the line rises from left to right, while a negative slope means it falls from left to right.