write the equation of the line in fully simplified slope-intercept form.\nanswer attempt 1 out of 2\nanswer:

Explanation:

Step1: Recall 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 $x = 0$, $y=2$. So, $b = 2$.

Step3: Calculate the slope ($m$)

The slope $m$ is calculated using the formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points on the line. For example, when $x = 0$, $y = 2$ (point $(0,2)$) and when $x = 1$, $y=3$ (point $(1,3)$). Then $m=\frac{3 - 2}{1 - 0}=\frac{1}{1}=1$. We can also check with another pair of points. Let's take $(0,2)$ and $(- 2,0)$. Then $m=\frac{0 - 2}{-2-0}=\frac{-2}{-2} = 1$.

Step4: Write the equation

Substitute $m = 1$ and $b = 2$ into the slope - intercept form $y=mx + b$. We get $y=x + 2$.

Answer:

$y=x + 2$