Find the equation of the linear function represented by the table below in slope-intercept form.
In order to find the equation of the linear function, we need to find the slope and y-intercept.
Looking at the table:
x | y
-----
2 | 3
4 | 7
6 | 11
We can see that the slope between the points (2, 3) and (4, 7) is:
(m = (7 - 3)/(4 - 2) = 4/2 = 2)
Since all the points in the table lie on a straight line, we know that the slope is consistent throughout. Therefore, the slope of the linear function is 2.
Now we need to find the y-intercept. We can do this by picking any point on the line and using the slope to find the y-intercept.
Using the point (2, 3):
y = mx + b
3 = 2(2) + b
3 = 4 + b
b = -1
Therefore, the y-intercept of the linear function is -1.
Using the slope-intercept form of a linear function (y = mx + b) and plugging in the values we found, we can write the equation of the linear function represented by the table as:
y = 2x - 1