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

Question

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.