The linear function f is f(x)= 5/3 x− 13/3.
To write a linear function f given two points (x1 ,y1 ) and (x2 ,y2), you can use the slope-intercept form of a linear equation:
f(x)=mx+b
where:
m is the slope of the line, and
b is the y-intercept.
To find the slope (m), use the formula:
m = y_2 -y_1 / x_2- x_1
Given f(2)=−1 and f(5)=4, you can use these points to find the slope:
m= 4−(−1)/5−2
m= 5/3
Now that you have the slope (m), you can use one of the points to find the y-intercept (b). Let's use the point
(2,−1):−1= 5/3 (2)+b
Solving for b:
−1= 10 +b/3
b=−1− 10/3
b=− 13/3
So, the linear function f is:
f(x)= 5/3 x− 13/3
Question
How do you write a linear function f with the values f(2)=−1 and f(5)=4?