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?

A. (6,3)

B. (4,4)

C. (8,0)

D. (1,3)

Answer 1

To find which point is on the line with the greatest slope, we need to calculate the slope of the line that passes through each point and the origin (0,0). The slope \( m \) of a line that passes through the origin and a point \((x,y)\) can be calculated using the formula:

\[
m = \frac{y}{x}
\]

Now, we will calculate the slope for each of the given points:

A. For the point (6, 3):
\[
m = \frac{3}{6} = \frac{1}{2} = 0.5
\]

B. For the point (4, 4):
\[
m = \frac{4}{4} = 1
\]

C. For the point (8, 0):
\[
m = \frac{0}{8} = 0
\]

D. For the point (1, 3):
\[
m = \frac{3}{1} = 3
\]

Now we have the slopes for each line:
- A: \( m = 0.5 \)
- B: \( m = 1 \)
- C: \( m = 0 \)
- D: \( m = 3 \)

The greatest slope is \(3\), which corresponds to point D (1, 3).

Thus, the point on the line with the greatest slope is:

**D. (1, 3)**