Question

which equation represents the graphed function?
\\( y = -2x + 3 \\)
\\( y = 2x + 3 \\)
\\( y = \frac{1}{2}x + 3 \\)
\\( y = -\frac{1}{2}x + 3 \\)

Explanation:

Step1: Identify y-intercept

The line crosses the y-axis at $(0, 3)$, so $b=3$ (slope-intercept form $y=mx+b$).

Step2: Calculate slope m

Use points $(0,3)$ and $(1,1)$.
$m=\frac{y_2-y_1}{x_2-x_1}=\frac{1-3}{1-0}=-2$

Step3: Build the equation

Substitute $m=-2$ and $b=3$ into $y=mx+b$.
$y=-2x+3$

Answer:

$y=-2x+3$