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. \( y = -\frac{2}{5}x + 3 \)
1 answer