Question

write an equation for this line in slope-intercept form. 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: Determine the slope ($m$)

For the line in the graph, we can see that for every 1 unit we move to the right (change in $x = 1$), we move up 1 unit (change in $y = 1$). The slope $m=\frac{\text{change in }y}{\text{change in }x}=\frac{1}{1} = 1$.

Step3: Determine the y - intercept ($b$)

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 $b = 2$.

Step4: Write the equation

Substitute $m = 1$ and $b = 2$ into the slope - intercept form $y=mx + b$. We get $y=1\times x+2$, which simplifies to $y=x + 2$.

Answer:

$y=x + 2$