Let f(x) be a linear function with f(1) = 2 and f(3) = 8. Find f(5)
How do u solve it like the steps
f changes by 6 when x changes by 2, so the slope is 6/2 = 3.
So, f(x) = 3x+b
Since f(1)=2, b = -1
f(x) = 3x-1
Would the answer be 16?
Cause if f(x)=3x-1
F(5) would be 3(5)-1
Which is 14
But someone told me the answer was 16
someone might be wrong
To solve for f(5) for a linear function with given values f(1) = 2 and f(3) = 8, you need to determine the equation of the linear function first.
Step 1: Identify the slope (m) of the linear function.
The slope (m) of a linear function can be found using the formula:
m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are any two points on the linear function.
In this case, you can plug in the values for f(1) = 2 and f(3) = 8 into the slope formula:
m = (8 - 2) / (3 - 1)
m = 6 / 2
m = 3
Step 2: Determine the equation of the linear function.
The equation of a linear function is in the form of y = mx + b, where m is the slope and b is the y-intercept.
Since you now have the slope (m = 3) and two points (1, 2) and (3, 8) on the linear function, you can use the point-slope formula to find the y-intercept (b):
y - y1 = m(x - x1)
Using the point (1, 2):
y - 2 = 3(x - 1)
y - 2 = 3x - 3
y = 3x - 3 + 2
y = 3x - 1
So, the equation of the linear function is f(x) = 3x - 1.
Step 3: Substitute x = 5 into the equation to find f(5).
Substituting x = 5 into the equation f(x) = 3x - 1:
f(5) = 3(5) - 1
f(5) = 15 - 1
f(5) = 14
Therefore, f(5) = 14.