Write the function represented by the table as an equation
x. y.
-2. 7
3. 27
5. 35
Find the slopes between points:
(27-7)/(3+2) = 4
(35-27)/(5-3) = 4
So, start with y = 4x
That doesn't quite fit, so find what you have to add to each 4x value to bring it into line.
(-2, 7), (3, 27), (5, 35).
Y = mx+b,
m = (27-7)/(3+2) = 20/5 = 4.
(-2, 7).
Y = 4*(-2) + b = 7,
-8+b = 7,
b = 15.
Eq: Y = 4x + 15.
To write the function represented by the table as an equation, we need to determine the pattern or relationship between the values of x and y.
Looking at the table, we can observe that the value of y is obtained by multiplying the value of x by a certain number and then adding another number. Let's find this pattern:
When x = -2:
y = (multiplying factor) * -2 + (constant term)
7 = (multiplying factor) * -2 + (constant term)
When x = 3:
y = (multiplying factor) * 3 + (constant term)
27 = (multiplying factor) * 3 + (constant term)
When x = 5:
y = (multiplying factor) * 5 + (constant term)
35 = (multiplying factor) * 5 + (constant term)
To find the multiplying factor and the constant term, we can subtract the second equation from the third equation and the first equation from the second equation:
27 - 7 = (multiplying factor) * (3 - (-2))
20 = (multiplying factor) * 5
multiplying factor = 20 / 5 = 4
Similarly,
35 - 27 = (multiplying factor) * (5 - 3)
8 = (multiplying factor) * 2
multiplying factor = 8 / 2 = 4
Now, we can substitute the multiplying factor into one of the equations to find the constant term:
7 = 4 * (-2) + (constant term)
7 = -8 + (constant term)
constant term = 7 + 8 = 15
The equation that represents the function is:
y = 4x + 15