x y
3 6
4 7
5 8
6 9
7 10
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
In order to determine whether the given data can be modeled by a linear or exponential function, let's first plot the points on the coordinate plane:
(x,y)
(3,6)
(4,7)
(5,8)
(6,9)
(7,10)
From the graph, it is evident that the relationship between x and y is linear. Therefore, we can use a linear function (y = mx + b) to model the data.
To find the slope (m) of the linear function, we can use the formula:
m = (change in y) / (change in x)
Using the first two points (3,6) and (4,7):
m = (7 - 6) / (4 - 3)
m = 1 / 1
m = 1
So far, our linear function is y = 1x + b.
To find the y-intercept (b), we can substitute the values of one of the points (let's use (3,6)) into the equation:
6 = 1(3) + b
6 = 3 + b
b = 6 - 3
b = 3
Therefore, the linear function that models the given data is:
y = x + 3