Question

Write an equation for the graph-Careful with the x-axis

Answer 1

Answer:

$y=\frac{1}{2}x +2$

Step-by-step explanation:

$y=\frac{1}{2}x +2$ is the equation for the graphed function.

Slope-intercept form

Slope-intercept form is a form a linear equation is written, especially used to when graph the equation. Slope-intercept form is $y=mx+b$. $m = slope, b =$ y-intercept.

Slope is calculated by Δy/Δx, or the change of y / the change of x. By looking at a graph, you can also find the slope of rise/run, which is the increase or decrease in y-coordinates / increase or decrease in x-coordinates.

Y-intercept is where a function intersects the y-axis.

We see that $b=2$ as the line intersects the y-axis at $(0,2)$. From any point graph, you can move to the next point using rise/run. In this case, we will start from $(0,2)$. We see that we increase in y-coordinates by 1 unit and increase in x-coordinates by 2 units to get to $(2,3)$. Same applies when going to the next point, $(3,4)$. We see that slope is a constant rate of change. Thus, rise/run $= \frac{1}{2}$. $m=\frac{1}{2}$.

Therefore,

$y=\frac{1}{2} +2$ is the equation for the graphed function.