Final answer:
To find a linear function f with given values, first calculate the slope using the two points provided, then use one point to determine the y-intercept. The equation for f is then determined using the slope and y-intercept.
Step-by-step explanation:
To write a linear function f with the given values f(6)=8 and f(9)=3, we first need to find the slope of the line. The slope (m) is determined by using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the given points. For our function, these points are (6,8) and (9,3).
Let's calculate the slope:
m = (3 - 8) / (9 - 6) = (-5) / 3
Now we have the slope of the line. To find the y-intercept (b), we can use one of the points and the slope in the slope-intercept form of a linear equation, y = mx + b.
This gives us:
8 = (-5/3)(6) + b
8 = -10 + b
b = 18
Therefore, our linear function is f(x) = -5/3x + 18.
A linear function is a function which forms a straight line in a graph. It is generally a polynomial function whose degree is utmost 1 or 0. Although the linear functions are also represented in terms of calculus as well as linear algebra. The only difference is the function notation. Knowing an ordered pair written in function notation is necessary too. f(a) is called a function, where a is an independent variable in which the function is dependent. Linear Function Graph has a straight line whose expression or formula is given by;
y = f(x) = px + q
It has one independent and one dependent variable. The independent variable is x and the dependent one is y. P is the constant term or the y-intercept and is also the value of the dependent variable. When x = 0, q is the coefficient of the independent variable known as slope which gives the rate of change of the dependent variable.