Question

what is the equation of this line in slope - intercept form?

1. $y = 5$
2. $y = 2x + 5$
3. $y = -2x + 5$
4. $y = -2x$

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: Analyze the y - intercept

From the graph (even though we can infer from the options), the y - intercept $b$ seems to be 5 (since when $x = 0$, $y=5$ for the correct line).

Step3: Analyze the slope

The line is decreasing (as $x$ increases, $y$ decreases), so the slope $m$ should be negative. Let's check the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. Take two points, say $(0,5)$ and $(1,3)$. Then $m=\frac{3 - 5}{1 - 0}=\frac{- 2}{1}=-2$.

Step4: Form the equation

Using $y=mx + b$, with $m=-2$ and $b = 5$, the equation is $y=-2x + 5$.

Answer:

C. $y=-2x + 5$ (assuming the options are labeled as A: $y = 5$, B: $y=2x + 5$, C: $y=-2x + 5$, D: $y=-2x$)