The image shows a problem asking to find two points on a line and the equation of the line. There is also a graph of a parabola with points and labels.

Task Breakdown:

• Part a: Find two points on the line.
• Part b: Find the equation of the line.

From the graph, it looks like the line starts at the origin $(0, -2)$ and passes through another point, possibly $(4, 1)$. These two points should help in both parts of the question.

Part (a): Find Two Points on the Line

From the graph, we can estimate:

• First point: $(0, -2)$
• Second point: $(4, 1)$

Part (b): Find the Equation of the Line

We will use the two points $(0, -2)$ and $(4, 1)$ to find the equation of the line. The formula for the slope $m$ of a line between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substituting the points $(0, -2)$ and $(4, 1)$:

$m = \frac{1 - (-2)}{4 - 0} = \frac{3}{4}$

Now that we know the slope is $\frac{3}{4}$, we can use the point-slope form of the line equation:

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

Substituting $m = \frac{3}{4}$ and $(x_1, y_1) = (0, -2)$:

$y - (-2) = \frac{3}{4}(x - 0)$

Simplifying:

$y + 2 = \frac{3}{4}x$

$y = \frac{3}{4}x - 2$

So, the equation of the line is:

$y = \frac{3}{4}x - 2$

Would you like more details or have any questions?

Follow-up Questions:

1. How would the equation of the line change if the slope was negative?
2. Can you verify the slope by using a different pair of points?
3. How would the line equation change if the y-intercept was different?
4. What is the geometric meaning of the slope in this problem?
5. How would you find the intersection of this line with another line?

Tip: Always double-check the coordinates of your points from the graph before calculating the slope to avoid errors!