Tyrell plans to run each week for 4 weeks - write a function equation from table
x/y
1/5
2/9
3/13
4/17
note that when x increases by 1, y increases by 4.
That means the slope of the line is 4, so the place to start is
y = 4x
That doesn't quite fit, so adjust it to bring it into line.
notice that for every increase of 1 in the x, the y increases by 4
so it must be y = 4x + ??
normally I would write this as y = 4x + b
now sub in one of the points, say (1,5)
5 = 4(1) + b
b = 1
y = 4x + 1
check to make sure the other points work in this equation
To write a function equation from a table, we look for a pattern between the input values (x) and the output values (y) in the table. In this case, we can see that for each week, the value of y is increasing by 4.
The pattern can be described as follows: for each week (x), the value of y is given by the equation y = 4x + b, where b is a constant.
To solve for the constant b, we can use one of the data points from the table. Let's use the first data point (x = 1, y = 5). Plugging these values into the equation, we get:
5 = 4(1) + b
5 = 4 + b
b = 1
Now that we have the value of b, the function equation becomes:
y = 4x + 1
So if Tyrell plans to run each week for 4 weeks, we can use this equation to calculate the number of miles (y) he runs in each week (x).