What is the rule for the function shown in the table?
x -1, 0, 1, 2
y -2, 1, 4, 7
a. y=1/3x+1
b. y=3x+1
c. y=1/3x
d. y=1/2+1******
Please help
looks like (b) to me.
1/2 x would leave extra 1/2's at all the odd values of x.
x1 = - 1
x2 = 0
x3 = 1
x4 = 2
x2 - x1 = 0 - ( - 1 ) = 0 + 1 = 1
x3 - x2 = 1 - 0 = 1
x4 - x3 = 2 - 1 = 1
y1 = - 2
y2 = 1
y3 = 4
y4 = 7
y2 - y1 = 1 - ( - 2 ) = 1 + 2 = 3
y3 - y2 = 4 - 1 = 3
y4 - y3 = 7 - 4 = 3
Since both x and y increase by a constant difference ( x increases by 1, and y increases by 3 ), this is a linear function.
You can think of it as if given two points. Let's take the first two:
( - 1 , - 2 ) and ( 0 , 1 )
Find ind the slope:
m = ( y2 - y1 ) / ( x2 - x1 )
m = [ 1 - ( - 2 ) ] / [ 0 - ( - 1 ) ]
m = ( 1 + 2 ) / ( 0 + 1 )
m = 3 / 1
m = 3
Using point slope form with the first point ( - 1 , - 2 )
y – y1 = m ( x – x1 )
y - ( - 2 ) = 3 [ x - ( - 1 ) ]
y + 2 = 3 ( x + 1 )
y + 2 = 3 x + 3 Subtract 2 to both sides
y + 2 - 2 = 3 x + 3 - 2
y = 3 x + 1
Proof :
x = - 1
y = 3 x + 1 = 3 * ( - 1 ) + 1 = - 3 + 1 = - 2
x = 0
y = 3 x + 1 = 3 * 0 + 1 = 0 + 1 = 1
x = 1
y = 3 x + 1 = 3 * 1 + 1 = 3 + 1 = 4
x = 2
y = 3 x + 1 = 3 * 2 + 1 = 6 + 1 = 7
Answer b
THank you soooo much! I see now
They are correct!
y= 3x + 1 is right
To determine the rule for the function shown in the table, we can look for a pattern in the values of x and y.
In this case, we can see that as x increases by 1, y also increases by 3.
To find the relationship between x and y, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
To find the slope, we can calculate the difference in the y-values and divide it by the difference in the x-values.
Using the points (-1, -2) and (0, 1) from the table, we can calculate the slope as follows:
m = (y2 - y1) / (x2 - x1)
m = (1 - (-2)) / (0 - (-1))
m = 3 / 1
m = 3
So, the slope of the function is 3.
Next, we need to find the value of the y-intercept (b).
Using the points (0, 1), we can substitute the values of x and y into the equation and solve for b:
1 = 3(0) + b
1 = b
Therefore, the y-intercept (b) is 1.
Now we can write the equation for the function:
y = 3x + 1
Comparing this equation to the given options, we can see that the correct answer is:
b. y = 3x + 1