Find the equation of the linear function represented by the table below in slope-intercept form.
X 0 1 2 3 4
Y -1 9 19 29 39
To find the equation of the linear function in slope-intercept form, we first need to find the slope and the y-intercept.
Using the formula for the slope, which is given by the difference in the y-coordinates divided by the difference in the x-coordinates, we can calculate the slope as:
slope = (change in y) / (change in x) = (y2 - y1) / (x2 - x1)
Let's consider the points (0, -1) and (1, 9):
slope = (9 - (-1)) / (1 - 0) = 10 / 1 = 10
Next, we need to find the y-intercept, which is the value of y when x = 0. From the table, we see that when x = 0, y = -1. Therefore, the y-intercept is -1.
Now that we have the slope (10) and the y-intercept (-1), we can write the equation of the linear function in slope-intercept form:
y = mx + b
where m is the slope and b is the y-intercept.
Substituting the values of m and b, we get:
y = 10x - 1
So, the equation of the linear function represented by the table in slope-intercept form is y = 10x - 1.