How do you find the slope of the secant lines of #f(x) = -3x + 2 # through the points: (-4,(f(-4)) and (1,f(1))?

Answer 1

#-3#

Find the points' #y#-values by evaluating #f(-4)# and #f(1)#:
#f(-4)=-3(-4)+2=12+2=14#
#f(1)=-3(1)+2=-3+2=-1#
The two points on the secant line are #(-4,14)# and #(1,-1)#.
The slope #m# can then be found using the slope equation:
#m=(Deltay)/(Deltax)=(14-(-1))/(-4-1)=15/(-5)=-3#
This should make sense, since #f(x)# is a line. The secant line, which passes through two points on #f(x)#, will have to be the exact same as #f(x)#--there's no other way a line can intercept two points.
Since the secant line is identical to #f(x)#, we can tell that they will have the same slope, and the slope of #f(x)=-3x+2# is #-3#.
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Answer 2

To find the slope of the secant line between two points on the graph of a function ( f(x) ), you use the formula:

[ \text{Slope} = \frac{{f(x_2) - f(x_1)}}{{x_2 - x_1}} ]

Where ( (x_1, f(x_1)) ) and ( (x_2, f(x_2)) ) are the given points.

For the function ( f(x) = -3x + 2 ) and the given points ( (-4, f(-4)) ) and ( (1, f(1)) ), plug the x-values into the function to find the corresponding y-values, and then use the formula to calculate the slope.

[ f(-4) = -3(-4) + 2 = 14 ] [ f(1) = -3(1) + 2 = -1 ]

Now, plug these values into the formula:

[ \text{Slope} = \frac{{-1 - 14}}{{1 - (-4)}} = \frac{{-15}}{{5}} = -3 ]

So, the slope of the secant line through the points ( (-4, f(-4)) ) and ( (1, f(1)) ) is ( -3 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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