Question

Graph the line that passes through the point (3,1) and has a y-intercept of 2.
Select points on the graph to plot them.

Complete the sentence.
The slope of the line is
–
1
3
–
3
–
1
3
1
3
3
, and the zero is
6
–
3
2
3
6
.

Answer 1

To graph the line that passes through the point (3, 1) and has a y-intercept of 2, we start by writing the equation of the line in slope-intercept form, \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

1. The y-intercept, \( b \), is given as 2. This means the line crosses the y-axis at (0, 2).

2. The line also passes through the point (3, 1). We can calculate the slope \( m \) using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Here, \( (x_1, y_1) = (0, 2) \) and \( (x_2, y_2) = (3, 1) \):
\[
m = \frac{1 - 2}{3 - 0} = \frac{-1}{3}
\]

So, the equation of the line is:
\[
y = -\frac{1}{3}x + 2
\]

Now, let's clear things up for the complete statement.

- The slope of the line is **–1/3**.
- To find the zero (x-intercept) of the line, we set \( y = 0 \):
\[
0 = -\frac{1}{3}x + 2
\]
Rearranging gives:
\[
\frac{1}{3}x = 2 \implies x = 2 \times 3 = 6
\]

Thus, the zero is **6**.

Final Completion:
The slope of the line is **–1/3**, and the zero is **6**.