Question

write the equation of the line in fully simplified slope-intercept form.

Explanation:

Step1: Identify y-intercept

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

Step2: Calculate slope $m$

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

Step3: Substitute into slope-intercept form

Slope-intercept form is $y=mx+b$. Substitute $m=1$ and $b=1$.
$y=1x+1$

Step4: Simplify the equation

Simplify $1x$ to $x$.
$y=x+1$

Answer:

$y=x+1$