Answer:
f(0) = 2
f(x) = 4x + 2
Step-by-step explanation:
You can see that the consecutive x-values are producing y-values that increase by 4 each time. Since the change in y is the same every time, we know this is a linear graph because in a continuous linear graph the slope does not change.
We can use the equation for a line: y = mx + b,
where m is the slope and b is the y-intercept.
The slope [m] is calculated by [change in y]/[change in x]. The y-values are increasing by 4 each time x increases by 1. m = 4/1 = 4.
Once we have found the slope, we can find the value for f(0). The line graph has a positive slope, so to find the value at x=0, we would subtract 4, moving backwards along the line.
6-4 = 2
The y-intercept on a line is the y-value for which x = 0. In this case we have already solved for the y-intercept, f(0) = 2.
Now plug the values into the formula.
y = mx + b
