Question

the diagram shows the graph of the line m
which equation represents this line?
\\( y = \frac{1}{2}x + 2 \\)
\\( y = -\frac{1}{2}x + 2 \\)
\\( y = -2x + 1 \\)
\\( y = 2x + 1 \\)

Explanation:

Step1: Identify y-intercept

The line crosses the y-axis at $(0,1)$, so $b=1$.

Step2: Calculate slope

Use two points $(0,1)$ and $(1,3)$.
Slope $m=\frac{3-1}{1-0}=2$

Step3: Write line equation

Substitute $m=2, b=1$ into $y=mx+b$:
$y=2x+1$

Answer:

D. $y = 2x + 1$