Final answer:
The equation of a linear function with a slope of 3 that passes through the point (2, 7) is found to be f(x) = 3x + 1 after calculating the y-intercept to be 1 using the given point and slope. So, the correct answer is (a) f(x) = 3x + 1.
Step-by-step explanation:
The equation of a linear function with a slope of 3 that passes through the point (2, 7) can be found using the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept.
In this case, we are given the slope m = 3 and a point on the line (2, 7).
Hence, we need to find the value of b by substituting the slope and the coordinates of the point into the slope-intercept equation.
Starting with the point-slope form and inserting our known values:
7 = 3(2) + b
7 = 6 + b
b = 7 - 6
b = 1
Now that we know b = 1, we can write the final equation of the line as:
f(x) = 3x + 1
Therefore, the correct answer is (a) f(x) = 3x + 1.
Question: Which is the equation of the function? The function f(x) represents a linear function with a slope of 3, and it passes through the point (2, 7).
a) ( f(x) = 3x + 1 )
b) ( f(x) = 3x - 11 )
c) ( f(x) = 11x + 1 )
d) ( f(x) = |x-11| - 4 )