Question

what is the slope - intercept equation of the line below? a. $y = 2x + 3$ b. $y = -2x + 3$ c. $y = 2x - 3$ d. $y = -2x - 3$

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: Determine the y - intercept

The y - intercept is the point where the line crosses the y - axis. From the graph, the line crosses the y - axis at $(0,-3)$. So, $b=-3$.

Step3: Determine the slope

The slope $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points on the line. We know the y - intercept is $(0, - 3)$ and we can see that when $x = 1$, $y=-1$ (by looking at the graph). So, using the points $(0,-3)$ and $(1, - 1)$:
$m=\frac{-1-(-3)}{1 - 0}=\frac{-1 + 3}{1}=\frac{2}{1}=2$.

Step4: Write the equation

Using the slope - intercept form $y=mx + b$ with $m = 2$ and $b=-3$, the equation is $y = 2x-3$.

Answer:

C. $y = 2x-3$