I had to repost this since I hit the submit button by mistake
Use patterns or a linear equation to complete the table.
column x 1,3,5,10,50,100
column y -1,3,7,?,?,?
I tried several combinations using -3,2,and -1 in place of m but still not coming out right.
Our options for the question marks
a)17,97,197
b)17,37,97
c)-10,-50,-100
d)23,97,197
Help please
"I tried several combinations using -3,2,and -1 in place of m but still not coming out right."
Are you missing part of this problem?
There is no 'm' anywhere in your posted problem to replace?
since you say it is "linear", let
y = mx + b
using the 2nd and 3rd data values
3 = 3m + b
7 = 5m + b
subtract them
4 = 2m
m=2
into the first
3 = 6 + b
b = -3
equation:
y = 2x - 3
the first data point satisfies this.
so now when x=10
y = 17
when x=50
y = 97
when x=100
y = 197
looks like a)
To complete the table using patterns or a linear equation, we need to identify the relationship between the values of x and y.
Looking at the given values, we can notice that the difference between consecutive x-values (1, 3, 5) is always 2, and the corresponding y-values (-1, 3, 7) are increasing by 4 each time. This suggests a linear relationship between x and y.
To find the equation of the line, we can use the slope-intercept form: y = mx + b, where m represents the slope and b represents the y-intercept.
To calculate the slope (m), we can use any two points from the table. Let's choose the first two points: (1, -1) and (3, 3).
m = (change in y)/(change in x) = (3 - (-1))/(3 - 1) = 4/2 = 2
Now that we have the slope, we can substitute it into the equation y = mx + b and solve for b using any point from the table. Let's use the point (1, -1).
-1 = 2(1) + b
-1 = 2 + b
b = -3
So, we have the equation for the linear relationship between x and y:
y = 2x - 3
Now, let's use this equation to fill in the missing y-values in the table:
For x = 10:
y = 2(10) - 3 = 17
For x = 50:
y = 2(50) - 3 = 97
For x = 100:
y = 2(100) - 3 = 197
Comparing these calculated values with the provided options, we can see that the answer is:
a) 17, 97, 197