Look at this table:
x y
3
–
16
4
–
21
5
–
26
6
–
31
7
–
36
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
Looking at the data, we can see that the value of y is increasing by a constant difference of 5 for each increase in x. This suggests that a linear function can model the data.
To find the equation of the linear function, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept.
Let's determine the values of m and b:
To find the slope (m), we can take any two points from the data. Let's take the points (3, 16) and (4, 21):
m = (y2 - y1)/(x2 - x1)
= (21 - 16)/(4 - 3)
= 5/1
= 5
Now we substitute the slope and any point from the data (let's use the point (3, 16)) into the equation to find b:
y = mx + b
16 = 5(3) + b
16 = 15 + b
b = 16 - 15
b = 1
Therefore, the linear function that models the data is:
y = 5x + 1.