Help: I need an equation for the following problems:
When x=25, y=?
In the function table the values for x are:
x = 3,5,7,9 and y = 8,14,20.26
#2
When x=8, y=?
In the function table the values for x are:
x = 0,2,4,6 and y = 8,18,28,38
In the first case, each increase of 2 in x increases y by 6 (three times as much as the increase in x). To get from x=9 to x=25, x must increasae by 16, so y must increase by 48, from 26 to 74.
#2 can be done the same way, and is even easier. Increase x by 2 and y must increase by 10. You don't need the equation.
Could you break this down, step by step - and the teacher requires and equation for both
Thanks
from the first set of data, select two ordered pairs,
e.g. (3,8) and (5,14)
slope =(14-8)/(5-3)
= 3
so the equation is y = 3x + b
but (3,8) lies on this so
8=3(3)+b
b=-1
and the equation is
y=3x-1
so when x=25
y=3(25)-1
= 74
do the second one the same way
Thanks so much - I do understand the logic - is there an easier way to set up this equation fro a 5th grader
2x-3(x+4)= -5
(1/3)y2+12=5x
To find an equation that represents the relationship between x and y in the given problems, we need to determine the pattern or rule that connects the values of x and y in the function table.
For Problem #1:
The given function table shows that as x increases by 2 (from 3 to 5, from 5 to 7, and from 7 to 9), y increases by 6 (from 8 to 14, from 14 to 20, and from 20 to 26). This indicates a linear relationship between x and y.
To find the equation, we need to determine the slope (m) and the y-intercept (b) of the linear function.
Slope (m):
The slope of a line can be calculated using the formula:
m = (change in y) / (change in x)
Let's calculate the slope using the points (3, 8) and (5, 14):
m = (14 - 8) / (5 - 3)
m = 6 / 2
m = 3
The slope of the linear function is 3.
Y-intercept (b):
To find the y-intercept, we can substitute the values of x and y from any point in the table into the equation y = mx + b and solve for b.
Using the point (3, 8):
8 = 3(3) + b
8 = 9 + b
b = 8 - 9
b = -1
The y-intercept of the linear function is -1.
Therefore, the equation representing the relationship between x and y in Problem #1 is:
y = 3x - 1
For Problem #2:
Similarly, the given function table shows a linear relationship between x and y.
Using the points (0, 8) and (2, 18) to calculate the slope:
m = (18 - 8) / (2 - 0)
m = 10 / 2
m = 5
The slope of the linear function is 5.
To find the y-intercept, we can use the point (0, 8):
8 = 5(0) + b
b = 8
The y-intercept of the linear function is 8.
Therefore, the equation representing the relationship between x and y in Problem #2 is:
y = 5x + 8
Now, we can use these equations to find the values of y when x is given.
For Problem #1:
When x = 25, we substitute x = 25 into the equation:
y = 3(25) - 1
y = 75 - 1
y = 74
Therefore, when x = 25, y = 74.
For Problem #2:
When x = 8, we substitute x = 8 into the equation:
y = 5(8) + 8
y = 40 + 8
y = 48
Therefore, when x = 8, y = 48.