Write a linear function f with the values f(0)=−3 and f(7)=11.

 f(x)= 2x -3

Step-by-step explanation:

Using the given information we can come up with two points that will be use to find the slope and y-intercept.  

If you input 0 you get -3  so the point will be (0,-3)

If you input 7  you get 11  so the point will be (7,11)

Now use the points to find the difference in their y coordinates and divide it by the difference in their x coordinates to find the slope.

y coordinates:  -3 - 11 = -14

x coordinates:  0 - 7 = -7

  -14/-7 = 2

Since the slope is two, we will use the slope intercept formula (y = mx +b) to find the b which is the y intercept.

Use one of the points and input its x and y coordinates into the formula including the slope to solve for b.

-3= 2(0) +b

-3 = 0 + b

b = -3  

f(x) is the same as y in the formula, meaning that the equation will be  

 f(x) = 2x -3