Answer:
[tex]y=\frac{1}{2}x+\frac{3}{2}[/tex]
Step-by-step explanation:
Slope-intercept form: [tex]y=mx+b[/tex] when [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept (the y-coordinate of the point where the line crosses the y-axis)
1) Find the slope ([tex]m[/tex])
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] when the given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
We can use any two points on the line to plug into this equation, but it's often easiest to use points that have whole-number coordinates. For example, we can use the points (1,-1) and (3,0).
[tex]m=\frac{0-(-1)}{3-1}[/tex]
Two negatives make a positive
[tex]m=\frac{0+1}{3-1}\\m=\frac{1}{2}[/tex]
So far, our equation looks like this:
[tex]y=\frac{1}{2}x+b[/tex]
2) Find the y-intercept ([tex]b[/tex])
We're told to approximate the y-intercept based on what appears to be true in the graph. In the graph, we can see that the y-intercept appears to occur when y=-1.5, or when y=[tex]-\frac{3}{2}[/tex]. Therefore, [tex]b=\frac{-3}{2}[/tex].
Now, after plugging both [tex]m[/tex] and [tex]b[/tex] into our equation, our final equation looks like this:
[tex]y=\frac{1}{2}x+\frac{3}{2}[/tex]
I hope this helps!
