Question

write the equation of the line in fully simplified slope-intercept form.
answer attempt 2 out of 2
answer: y = x + 2

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

The y - intercept is the point where the line crosses the y - axis. From the graph, the line crosses the y - axis at $(0,2)$, so $b = 2$.

Step3: Calculate the slope

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, $(0,2)$ and $(1,3)$. Then $m=\frac{3 - 2}{1 - 0}=\frac{1}{1}=1$.

Step4: Write the equation

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

Answer:

$y=x + 2$