Question

Answer the questions from the graph. (4 points) What is the y-intercept? Response area What is the slope? Response area What is the equation of the line in slope-intercept form? Response area This is a Response area relationship.

the pin pointed points are, -4 is on the x axis, -2, 1 and 2 on the y axis and 2, 3

Answer 1

To provide accurate answers to your questions, I need to clarify the given points from the graph. Based on your input:

1. **Y-Intercept:** This is the point where the line intersects the y-axis. From the information provided, you mention points on the y-axis being at -2, 1, and 2. If the line intersects the y-axis at y = 2, then the **y-intercept is (0, 2)**.

2. **Slope (m):** The slope is calculated as the rise over run between two points on the line. If we take two points from your description, for example, (0, 2) (the y-intercept) and (-4, -2), we can find the slope using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using points (0, 2) and (-4, -2):
\[
m = \frac{-2 - 2}{-4 - 0} = \frac{-4}{-4} = 1
\]
Thus, the **slope is 1**.

3. **Equation of the Line in Slope-Intercept Form:** The slope-intercept form of a line is given by the equation:
\[
y = mx + b
\]
Where \(m\) is the slope and \(b\) is the y-intercept. Here, with \(m = 1\) and \(b = 2\), the equation is:
\[
y = 1x + 2 \quad \text{or simply} \quad y = x + 2
\]

4. **Type of Relationship:** From the information provided, since the slope is positive, this indicates that there is a direct (positive) linear relationship between the x and y variables.

To summarize:
- **Y-Intercept:** (0, 2)
- **Slope:** 1
- **Equation of the Line:** \(y = x + 2\)
- **Type of Relationship:** Positive linear relationship.