which function rule represents the data in the table below.
input (x) 1, 2, 3, 4, 5
output (y) 9, 14, 19, 24, 29
y = 4 + 5x
y = 3 + 6x
y = 5 + 4x
y = 6 + 3x
Show your work.
To find the function rule that represents the data in the table, we need to look for a pattern between the input and output values.
If we subtract the first output value (9) from the second output value (14), we get 5. Similarly, if we subtract the second output value (14) from the third output value (19), we get 5 again. This tells us that the output values are increasing by 5 for each increase in the input value.
Now we need to figure out the starting value (also known as the y-intercept) of the function. We can do this by looking at the table and noticing that when x=0 (which is not in the table), y=4. This means that the function starts at y=4.
Putting this all together, we get:
y = starting value + rate of change * input
y = 4 + 5x
Therefore, the function rule that represents the data in the table is y = 4 + 5x.
input x 1 2 3 4 5
output y 9 12 15 18 21
y=4+5x
y= 3+6x
y=5+4x
y=6+3x
plz help i need the answer
To find out which function rule represents the data in the table, we need to look for the relationship between the input and output values.
Based on the table, we can observe that as the input value increases by 1, the output value increases by 3. This tells us that the rate of change of the function is equal to 3.
Furthermore, when x = 0 (not shown in the table), the output value must be 6. This is because if the rate of change is 3 and we start at 6, the first output value when x = 1 must be 9 (6 + 3), which matches the table.
Substituting the rate of change (3) and the starting value (6) into the slope-intercept form of a linear function (y = mx + b) gives us:
y = 3x + 6
Therefore, the function rule that represents the data in the table is y = 3x + 6.
So, the correct answer is none of the provided options.
To determine which function rule represents the given data, we need to analyze the relationship between the input (x) and output (y) values in the table.
Looking at the given table:
input (x): 1, 2, 3, 4, 5
output (y): 9, 14, 19, 24, 29
We notice that as the input (x) increases by 1, the output (y) increases by 5.
To find the function rule, we can use the slope-intercept form of a linear function, which is y = mx + b, where m represents the slope and b represents the y-intercept.
From the given data, we can observe that the slope (m) is 5 since y increases by 5 for every increase of 1 in x.
To determine the value of the y-intercept (b), we can look at the starting point in the table when x = 1 and y = 9.
Substituting these values into the slope-intercept form, we get: 9 = 5(1) + b
Simplifying the equation, we have: 9 = 5 + b
To solve for b, we subtract 5 from both sides: b = 9 - 5 = 4
Now we have the slope (m) and y-intercept (b), so we can write the function rule:
y = 5x + 4
Comparing this equation to the given options, we can see that the correct function rule that represents the given data is:
y = 5 + 4x