Answer:
[tex]y = \frac{-1}{2} x+1[/tex]
Step-by-step explanation:
We are given the graph of an equation and want to find the equation of the line in y = mx + b form.
Let's start by finding the slope. The equation for slope is [tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]. We must find two points on the line to use for finding slope; let's use (0,1) and (4,-1).
[tex]m = \frac{1 - (-1)}{0-4} \\m=\frac{2}{-4} =\frac{-1}{2}[/tex]
So, we find that our slope is -1/2.
Now, let's find the y-intercept. When given a graph, we can easily find the y-intercept by noting the y-value when x = 0. In this case, the y-intercept is 1.
Lastly, we'll put all our values together to get [tex]y = \frac{-1}{2} x+1[/tex] as the equation for this graph.
