X|-1|0|1|2|
y|-2|1|4|7|
What is the rule for the function shown in the table?
A.y= 1/3x+1
B.y=3x+1
C.y=1/3x
D.y=1/2x+1
Is the answer B??
it is B
Thank you!!!😊
To find the rule for the function shown in the table, we need to determine the pattern or relationship between the values of x and y.
Looking at the x-values and their corresponding y-values, we can observe that as x increases by 1 unit, y increases by 3 units. This indicates a linear relationship between x and y.
To find the slope (m) of the line, we can choose any two points from the table and calculate the change in y divided by the change in x. Let's choose the points (0, 1) and (1, 4):
Change in y = 4 - 1 = 3
Change in x = 1 - 0 = 1
m = (Change in y) / (Change in x) = 3 / 1 = 3
Therefore, the slope of the line is 3.
To find the y-intercept (b) of the line, we can substitute any point from the table (0, 1) and the slope m into the slope-intercept form of a linear equation, y = mx + b, and solve for b.
Using the point (0, 1):
1 = 3(0) + b
1 = 0 + b
b = 1
Therefore, the y-intercept (b) is 1.
Putting it all together, the rule for the function shown in the table is y = 3x + 1.
Comparing this with the given answer choices:
A. y = 1/3x + 1 (incorrect)
B. y = 3x + 1 (correct)
C. y = 1/3x (incorrect)
D. y = 1/2x + 1 (incorrect)
The correct answer is B. y = 3x + 1.