Question

Four different lines are drawn on a coordinate plane. The lines all pass through the origin, and each line passes through one of the points listed below.


Which of the points is on the line with the greatest slope?
(4,4) (8,0) (1,3) (6,3)
A. 4,4

B. 1,3

C. 8,0

D. 6,3

Answer 1

To determine which point corresponds to the line with the greatest slope, we can calculate the slope for each line that passes through the origin and the given points. The slope of a line passing through the origin and a point \((x, y)\) is given by the formula:

\[
\text{slope} = \frac{y}{x}
\]

Let's calculate the slopes for each of the given points:

1. For point \((4, 4)\):
\[
\text{slope} = \frac{4}{4} = 1
\]

2. For point \((8, 0)\):
\[
\text{slope} = \frac{0}{8} = 0
\]

3. For point \((1, 3)\):
\[
\text{slope} = \frac{3}{1} = 3
\]

4. For point \((6, 3)\):
\[
\text{slope} = \frac{3}{6} = \frac{1}{2} = 0.5
\]

Now, we have the following slopes:

- Point \((4, 4)\): slope = 1
- Point \((8, 0)\): slope = 0
- Point \((1, 3)\): slope = 3
- Point \((6, 3)\): slope = 0.5

The greatest slope among these is for the point \((1, 3)\) which has a slope of 3.

Thus, the answer is:

**B. (1, 3)**