What is an equation for the function that gives the values in the table?
xl 2 l 3 l 4 l
yl10l13l16l
In other words, x-2, y-10, x-3 y-13, x-4 y-16
I'm sorry! I didn't notice that I published this more than once!
Check your previous post for solution.
To find an equation for the function that gives the values in the table, we need to determine the relationship between the x-values (xl 2 l 3 l 4 l) and the y-values (yl10l13l16l).
Let's start by looking at how the x-values change. We can see that as x increases by 1 (from 2 to 3, and from 3 to 4), the corresponding y-values increase by 3 (from 10 to 13, and from 13 to 16). This suggests that the relationship between x and y is a linear one.
To write the equation of a line, we need two pieces of information: the slope (m) and the y-intercept (b).
To find the slope (m), we can choose any two points from the table. Let's consider the points (2, 10) and (3, 13).
m = (change in y) / (change in x) = (13 - 10) / (3 - 2) = 3 / 1 = 3
So, the slope (m) is equal to 3.
Next, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
To find the y-intercept (b), we can substitute the coordinates of one of the points into the equation.
Using the point (2, 10):
10 = (3)(2) + b
10 = 6 + b
b = 10 - 6
b = 4
Therefore, the y-intercept (b) is equal to 4.
Finally, we can write the equation of the line in slope-intercept form using the values we found:
y = 3x + 4
So, the equation for the function that gives the values in the table is y = 3x + 4.