Question

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

Explanation:

Step1: Find the slope

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points on the line, say $(0,1)$ and $(1,3)$. Then $m=\frac{3 - 1}{1 - 0}=2$.

Step2: Find the y - intercept

The slope - intercept form of a line is $y=mx + b$, where $b$ is the y - intercept. From the graph, the line crosses the y - axis at the point $(0,1)$, so $b = 1$.

Step3: Write the equation

Substitute $m = 2$ and $b=1$ into $y=mx + b$. We get $y = 2x+1$.

Answer:

$y = 2x + 1$