If f(x) is a linear function such that f(4) = 3, with a slope of 1/2, what is the equation of f(x)?
A linear function follows the form f(x) = mx + b, where m is the slope and b the y-intercept.
We are given the point (4, 3) and that m = .5, so we can solve for b.
f(4) = 3 = .5(4) + b
So b = 1. The function is therefore f(x) = .5x + 1
f (×) = 4× +3
To find the equation of a linear function, we need to know the slope and the y-intercept. In this case, the slope is given as 1/2.
We also have a point on the line, (4, 3), where x = 4 and f(4) = 3.
Using the point-slope form of a linear equation, the equation of a line can be written as:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope. Plugging in the values we have:
y - 3 = (1/2)(x - 4)
Simplifying, we can distribute the (1/2):
y - 3 = (1/2)x - 2
Then we can isolate y by moving -3 to the other side of the equation:
y = (1/2)x - 2 + 3
Simplifying further:
y = (1/2)x + 1
So, the equation of f(x) is y = (1/2)x + 1.
To find the equation of a linear function, we need to know the slope and a specific point on the line. In this case, we have the slope (1/2) and the point (4,3).
To find the equation, we can use the slope-intercept form:
y = mx + b
Where:
y = the value of the function
m = slope of the line
x = the input value
b = y-intercept
We are given the slope (m = 1/2), and we know the point (4,3) lies on the line.
We can substitute the values into the equation to solve for b:
3 = (1/2)(4) + b
3 = 2 + b
b = 3 - 2
b = 1
Now we have the slope (1/2) and the y-intercept (1). We can plug these values into the slope-intercept form to get the equation of f(x):
y = (1/2)x + 1
So, the equation of f(x) is y = (1/2)x + 1.