Question

given a line passing through (0, 2) with slope -3, what is its equation?
y = -3x + 2
y = -3x - 2
y = 2x - 3
y = 3x + 2

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: Identify slope and y - intercept

We are given that the slope $m=-3$ and the line passes through the point $(0,2)$. The y - intercept $b$ is the y - coordinate of the point where the line crosses the y - axis. When $x = 0$, $y=b$. So, when $x = 0$, $y = 2$, which means $b = 2$.

Step3: Substitute m and b into the formula

Substitute $m=-3$ and $b = 2$ into the slope - intercept form $y=mx + b$. We get $y=-3x + 2$.

Answer:

A. $y = - 3x+2$