Question

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

Explanation:

Step1: Identify 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: Find the y - intercept ($b$)

The y - intercept is the value of $y$ when $x = 0$. From the graph, when $x = 0$, $y=1$. So, $b = 1$.

Step3: Calculate the slope ($m$)

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's choose two points on the line. We can use the points $(0,1)$ and $(1,2)$ (we can see from the graph that when $x = 1$, $y = 2$).
Substitute into the slope formula: $m=\frac{2 - 1}{1 - 0}=\frac{1}{1}=1$.

Step4: Write the equation

Substitute $m = 1$ and $b = 1$ into the slope - intercept form $y=mx + b$. We get $y=x + 1$.

Answer:

$y = x+1$