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)

Question

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. $y=-\frac{2}{5}x+3$