can someone please help me with this question?
Given the function f(x)=3x-9
Find the rate of the change between the stated values for x: 7 to 8
A. Find the equation of a secant line containg the given point (7,f,(7)) and (8,f,8))
B. Find the rate of change between the stated values for x: 7 to 8
z. f(x)=3x-9
b. rate of change is 3
explaination: find the two points (at x=7, and x=8).
then find the slope (f(8)-f(7)/(1))
then the equation is of the form y=slope*x+b. Put either point in, and solve fodr b.
Sure! I can help you with that.
To find the rate of change between the stated values for x (7 to 8), we can use the formula for the slope of a secant line. The secant line is a straight line that passes through two points on the graph of the function.
A. To find the equation of the secant line containing the given points (7, f(7)) and (8, f(8)), we need to calculate the slope of the line. The slope formula is:
slope = (f(8) - f(7)) / (8 - 7)
First, let's find the values of f(8) and f(7):
f(8) = 3(8) - 9 = 24 - 9 = 15
f(7) = 3(7) - 9 = 21 - 9 = 12
Now, substitute these values into the slope formula:
slope = (f(8) - f(7)) / (8 - 7)
= (15 - 12) / (8 - 7)
= 3 / 1
= 3
So the slope of the secant line is 3. Now, we can use this slope and one of the given points to find the equation of the secant line. Let's use the point (7, f(7)) = (7, 12).
Using the point-slope form of a line, the equation of the secant line can be written as:
y - 12 = 3(x - 7)
Simplifying this equation, we get the equation of the secant line:
y = 3x - 15
B. Now, let's find the rate of change between the values of x: 7 to 8. The rate of change is simply the slope of the secant line that we calculated earlier, which is 3. So the rate of change between x = 7 to x = 8 is 3.
I hope this helps! Let me know if you have any further questions.