Find the equation of the linear function represented by the table below in the slope-intercept form.
x: 0 1 2 3 4
y: 2 12 22 32 42
To find the equation of the linear function represented by the table, we need to determine the slope and the y-intercept.
First, let's find the slope (m). We'll use the formula:
m = (change in y) / (change in x)
The change in y is the difference between y-values for any two points, and the change in x is the difference between the corresponding x-values.
For example:
m = (12 - 2) / (1 - 0)
m = 10 / 1
m = 10
To find the y-intercept (b), we can choose any point from the table and substitute its coordinates (x, y) into the slope-intercept form equation: y = mx + b. Let's choose the point (0, 2).
2 = 10(0) + b
2 = 0 + b
b = 2
Now that we have the slope (m = 10) and the y-intercept (b = 2), we can write the equation of the linear function in slope-intercept form: y = 10x + 2.