can someone please help me with this question.
Given the funtion f(x)= 3x-9
a. find the rate of change between the two stated values for x: 7 to 8
b. find the equation of a secant line containing the given points: (7,f(7)) and (8,f(8))
I think I have (a)answered, just need help with b; please.
f(7) = 21-9 = 12
f(8) = 24-9 = 15
so the change in the range = 15-12 = 3
change in domain = 8-7 = 1
for every change of 1 in the x's there will be a change of 3 in the y's
or
rate of change is 3/1 = 3
b) from above, slope = 3
y = 3x + b
sub in (7,12)
12 = 3(7) + b
b = -9
y = 3x - 9 ahhh, the same as the original equation !
(since y = 3x-9 is a straight line, of course we are going to end up with the same equation for a "secant" between any two points on a straight line)
Of course! I can help you with part (b) of your question. To find the equation of a secant line containing two points, we can use the formula for the slope of a line.
In this case, the two points are (7, f(7)) and (8, f(8)). To find the slope of the line passing through these points, we can use the slope formula:
slope = (change in y) / (change in x)
To calculate the change in y, subtract the y-values of the two points:
Δy = f(8) - f(7)
To calculate the change in x, subtract the x-values of the two points:
Δx = 8 - 7
Now you can substitute these values into the slope formula:
slope = Δy / Δx
Finally, substitute the function f(x) = 3x - 9 into the equation to find f(8) and f(7). Then calculate the values and plug them into the slope equation.
Once you have the slope, you can use the point-slope form of a linear equation, y - y₁ = m(x - x₁), where (x₁, y₁) is one of the given points and m is the slope, to find the equation of the secant line.