Question

Four students drew graphs of a linear function. Which student drew a line with a slope of 3?

Analise
On a coordinate plane, a line goes through points (negative 3, 0) and (0, 1).

Benito
On a coordinate plane, a line goes through points (0, negative 1) and (1, 2).

Charlie
On a coordinate plane, a line goes through points (0, negative 3) and (0, 3).

Dariya
On a coordinate plane, a line goes through points (2, 3) and (3, 0).

Analise
Benito
Charlie
Dariya

Answer 1

To find which student drew a line with a slope of 3, we can calculate the slope (m) of the lines that each student drew using the slope formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Now, let's calculate the slope for each student:

1. **Analise**: The points are (-3, 0) and (0, 1).
\[
m = \frac{1 - 0}{0 - (-3)} = \frac{1}{3}
\]

2. **Benito**: The points are (0, -1) and (1, 2).
\[
m = \frac{2 - (-1)}{1 - 0} = \frac{2 + 1}{1} = \frac{3}{1} = 3
\]

3. **Charlie**: The points are (0, -3) and (0, 3). This line is vertical, and its slope is undefined.

4. **Dariya**: The points are (2, 3) and (3, 0).
\[
m = \frac{0 - 3}{3 - 2} = \frac{-3}{1} = -3
\]

From the calculations, we find that **Benito** is the student who drew a line with a slope of 3.