Question

Which function best represents the relationship shown in the graph?
Points on the graph: (7.5, 0) and (0,3)

A: y = -2/5x + 3

B: y = -2/5x + 7

C: y = -5/2x + 7

D: y = -5/2x + 3

Answer 1

To determine which function best represents the relationship shown in the graph with the points (7.5, 0) and (0, 3), we first need to find the slope of the line that passes through these two points.

We can use the slope formula, which is:

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

Let the points be \( (x_1, y_1) = (0, 3) \) and \( (x_2, y_2) = (7.5, 0) \).

Now substituting in the values:

\[
m = \frac{0 - 3}{7.5 - 0} = \frac{-3}{7.5} = -\frac{3}{7.5} = -\frac{3 \times 2}{7.5 \times 2} = -\frac{6}{15} = -\frac{2}{5}
\]

The slope \(m = -\frac{2}{5}\).

Next, we can use the slope-intercept form of the equation of a line, which is:

\[
y = mx + b
\]

We already determined \(m = -\frac{2}{5}\). Now we will use one of the points to find \(b\), the y-intercept. Let's use the point (0, 3):

Substituting \(x = 0\) and \(y = 3\):

\[
3 = -\frac{2}{5}(0) + b
\]
\[
b = 3
\]

Thus, the equation of the line is:

\[
y = -\frac{2}{5}x + 3
\]

Now we can compare this with the given options:

- A: \(y = -\frac{2}{5}x + 3\) ✔️ (this matches our equation)
- B: \(y = -\frac{2}{5}x + 7\)
- C: \(y = -\frac{5}{2}x + 7\)
- D: \(y = -\frac{5}{2}x + 3\)

The function that best represents the relationship shown in the graph is:

**A: \(y = -\frac{2}{5}x + 3\)**.