Question

Which function best represents the relationship shown in the graph? the graph shows a line with a y-intercept of (0, 3) and an x-intercept of (7.5, 0)
a. y=-\frac{2}{5}x+3
b. y=-\frac{2}{5}x+7
c. y=-\frac{5}{2}x+7
d. y=-\frac{5}{2}x+3

Answer 1

To determine the function that best represents the line with a y-intercept of (0, 3) and an x-intercept of (7.5, 0), we can start by finding the slope of the line.

The slope \( m \) can be calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points (0, 3) (y-intercept) and (7.5, 0) (x-intercept):
- \( (x_1, y_1) = (0, 3) \)
- \( (x_2, y_2) = (7.5, 0) \)

Plugging in the values:
\[
m = \frac{0 - 3}{7.5 - 0} = \frac{-3}{7.5} = -\frac{3}{7.5} = -\frac{3}{\frac{15}{2}} = -\frac{3 \cdot 2}{15} = -\frac{6}{15} = -\frac{2}{5}
\]

Now, we can use the slope and y-intercept to write the equation of the line in slope-intercept form, \( y = mx + b \):
\[
y = -\frac{2}{5}x + 3
\]

Comparing this with the answer choices, we find that the correct function is:

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