function rule

Question

Write a function rule for the table of values.

x y
0 1
1 3
2 5
-3 -5

Answer 1

the equation of a linear function is y=mx+b

where m is the slope and b is the y-intercept.

 

m = y₂-y₁/x₂-x₁

so if we consider points (0,1) and (1,3)

then m=(3-1)/(1-0)=2

slope of the function is 2.

 

when x=0, the value the function crosses the y axis is the y-intercept, b.

We can use the point (0,1)

 

1=m*0+b

1 = b, the y-intercept

 

Since we know m and b, then we can write the function as

y = 2x + 1