Use patterns or a linear equation to complete the table.
11) x y
1 -1
3 3
5 7
10 ?
50 ?
100 ?
I don't understand what I'm suppose to do! Please hep and explan well! Thank you!
X|Y
---
0|(-3)
1|-1
2|(1)
3|3
4|(5)
5|7
y=2x-3
when x=10, y=17
when x=50, y=97
when x=100, y=197
That is no where near what I need I need help please!
Thank you(:
Valerie,
Read what w said carefully
y = 2 x - 3 !!!
for any x, that gives you y
w noticed that all the given points sat in the straight line y = 2x-3
Now the wayt ot figure that out is to take the slope between any two points
like here
m = (7-3)/(5-3) = 4/2 = 2
so if there is a linear relation
y = 2 x + b
now what is b?
when x = 1, y = -1
-1 = 2 + b
so b = -3
now check to make sure that fits all points, then use it.
To complete the table, we can look for a pattern or use a linear equation to find the missing values for y.
One way to find a pattern is to observe the differences between consecutive x-values and y-values. Let's look at the differences for the given data:
Difference of x-values: 2, 2, 5, 40, 50
Difference of y-values: 4, 4, ?, ?, ?
By observing the differences of x and y, we can see that the difference between the x-values is increasing by 2 each time, and the difference between the y-values is constant at 4.
So, if we continue this pattern, the missing differences would be 55 for the x-values and 4 for the y-values.
Starting from the last known x-value (50), we can add the missing difference (55) to find the next x-value:
50 + 55 = 105
Similarly, starting from the last known y-value (7), we can add the missing difference (4) to find the next y-value:
7 + 4 = 11
Let's fill in the missing values in the table:
x y
1 -1
3 3
5 7
10 11
50 55
100 59
Alternatively, we can use a linear equation to find the relationship between x and y.
Let's start by finding the slope (m) using two of the given points:
m = (change in y) / (change in x)
Using (1, -1) and (3, 3):
m = (3 - (-1)) / (3 - 1)
m = 4 / 2
m = 2
Now, we can find the y-intercept (b) by substituting one of the points and the slope into the equation y = mx + b. Let's use (1, -1):
-1 = 2(1) + b
-1 = 2 + b
b = -1 - 2
b = -3
Now that we have the slope (m) and the y-intercept (b), we can find the missing y-values for the given x-values.
For x = 10:
y = mx + b
y = 2(10) + (-3)
y = 20 - 3
y = 17
For x = 50:
y = mx + b
y = 2(50) + (-3)
y = 100 - 3
y = 97
For x = 100:
y = mx + b
y = 2(100) + (-3)
y = 200 - 3
y = 197
Now, let's fill in the missing values in the table:
x y
1 -1
3 3
5 7
10 17
50 97
100 197
Either method (finding the pattern or using a linear equation) can be used to complete the table.