Answer: y=x+4
Step-by-step explanation:
The equation for a straight line can be written as y=mx+b, where m is the slope and b is the y-intercept (the value of y when x=0).
We can determine b just by looking at the value of y at x=0, which is y=4.
This quickly gives us y = mx + 4. This immediately eliminates two of the possible answers (the ones where b = -4).
All we need to do now is find the slope, m.
The slope of the line can be determined by calculating the "Rise/Run." That is the change in y (Rise) for each change in x (Run). Pick any two points. I'll choose (-2,2) and (2,6). Rise = (6-2)=4; Run = (2 - (-2)) = 4.
The Rise over the Run is 4/4, or 1. The graphed line has a slope of 1, so we can now write:
y = 1x + 4
Test this by entering any vlaue of x and see if this equation correctly returns tha same value as shown on the graph. E.g., when x = 6, will this equation correctly predict y as 10? It does, so let's go with y=x+4.
