SOLUTION: Find the slope of the graph of the linear function f f(5/2) = 7/2 f(4) = 6 I am a parent trying to answer my sons question and explain it to him Thanks

Question 243546: Find the slope of the graph of the linear function f
f(5/2) = 7/2
f(4) = 6
I am a parent trying to answer my sons question and explain it to him
Thanks
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Note: f(x) is used in place of y. So this means that the line goes through the two points (5/2,7/2) and (4,6)

First let's find the slope of the line through the points and

Note: is the first point . So this means that and .
Also, is the second point . So this means that and .

Start with the slope formula.

Plug in , , , and

Subtract from to get

Subtract from to get

Multiply the first fraction by the reciprocal of the second fraction.

Multiply and reduce.

So the slope of the line that goes through the points and is

Now let's use the point slope formula:

Start with the point slope formula

Plug in , , and

Distribute

Multiply

Add to both sides.

Combine like terms.

Simplify

So the equation that goes through the points and is

Notice how the graph of goes through the points and . So this visually verifies our answer.

Graph of through the points and

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find the slope of the graph of the linear function f
f(5/2) = 7/2
f(4) = 6
------------------
You have been given two points: (5/2,7/2) and (4,6)
-------------------
These points are in the form (x,y)
-------------------------
the slope = (change in the y values)/(change in the x values)
---
slope = [6 - (7/2))/(4 - (5/2))
slope = [(12/2) - (7/2)] / [(8/2)- (5/2)]
slope = (5/2)/(3/2)
Invert the denominator and multipl to get:
slope = (5/2)(2/3)
Cancel the 2 that is in the numerator and in the denominator to get:
slope = 5/3
========================
Cheers,
Stan H.
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