Question

A graph of a straight line is shown. The line passes through the points (-5, -2), (-3, 0), (-2, 1), (2, 3), and (5, 5). The x-axis ranges from -6 to 6, and the y-axis ranges from -6 to 6. Gridlines are visible. The line slants upward to the right.


The slope of the graph is (blank)
The y-intercept of the graph is (blank)

The equation of the graph in slope-intercept form is (blank)

This is a (blank) relationship.

Answer 1

To find the slope, y-intercept, and the equation of the line based on the points provided, let's analyze the information step-by-step.

1. **Calculate the slope (m):**
The slope (m) can be calculated using any two points on the line. We can use the points (-3, 0) and (2, 3) for this purpose.

The formula for the slope is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Plugging the points in:
\[
m = \frac{3 - 0}{2 - (-3)} = \frac{3}{2 + 3} = \frac{3}{5}
\]

2. **Find the y-intercept (b):**
We need to determine the y-intercept (b), which is the value of y when x = 0. We can use the slope-intercept form of a linear equation:
\[
y = mx + b
\]

We can substitute one of the points, say (-3, 0), to find b:
\[
0 = \frac{3}{5}(-3) + b
\]
\[
0 = -\frac{9}{5} + b
\]
\[
b = \frac{9}{5}
\]

3. **Write the equation of the line in slope-intercept form:**
Now that we have the slope (m = 3/5) and the y-intercept (b = 9/5), we can write the equation:
\[
y = \frac{3}{5}x + \frac{9}{5}
\]

4. **Determine the type of relationship:**
A line that trends upward to the right indicates a positive linear relationship between x and y.

Putting all of this together:

- The slope of the graph is **3/5**.
- The y-intercept of the graph is **9/5**.
- The equation of the graph in slope-intercept form is **y = (3/5)x + (9/5)**.
- This is a **positive** relationship.