Question

1. which of the following equations represents a line with a y-intercept of (0, -6) and a slope of \\(\frac{2}{3}\\)?

a. \\(y = -\frac{3}{2}x - 6\\)

b. \\(y = -\frac{2}{3}x + 6\\)

c. \\(y = -\frac{2}{3}x - 6\\)

d. \\(y = \frac{2}{3}x - 6\\)

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 $m = \frac{2}{3}$ and y-intercept $b = -6$, substitute into the formula: $y = \frac{2}{3}x - 6$.

Step3: Match with options

The resulting equation matches option d.

Answer:

d. $y = \frac{2}{3}x - 6$