Question

which equation represents a line with a slope of \\(\frac{5}{2}\\) and a \\(y\\)-intercept of \\(-\frac{8}{3}\\)?\
a \\(y = -\frac{8}{3x} + \frac{8}{3}\\)\
b \\(y = -\frac{5}{2}x + \frac{8}{3}\\)\
c \\(y = \frac{5}{2}x - \frac{8}{3}\\)\
d \\(y = \frac{5}{2x} - \frac{8}{3}\\)

Explanation:

Step1: Recall slope-intercept form

The slope-intercept form of a line is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Step2: Substitute given values

Given slope \( m = \frac{5}{2} \) and y-intercept \( b = -\frac{8}{3} \), substitute into the form: \( y = \frac{5}{2}x - \frac{8}{3} \).

Step3: Match with options

The resulting equation matches option C.

Answer:

C. \( y = \frac{5}{2}x - \frac{8}{3} \)