## linear function question

Algebra, Functions and equations, Circular functions and trigonometry, Vectors, Statistics and probability, Calculus. IB Maths SL Revision Notes

### linear function question

If the function $f(x)$ represents a straight line and it’s known that $f(2)=3$ and $f(-1)=4$, find the value of $f(10)$.
Jack

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Joined: Mon Jan 28, 2013 8:08 pm

### Re: linear function question

The equation of a straight line is of the form
$f(x)=ax+b$

where $a$ is the slope and $b$ is the y-intercept.

The slope can be found by the following formula:
$a=\frac{y_{2}- y_{1}}{ x_{2}- x_{1}}$ where $( x_{1}, y_{1}), ( x_{2}, y_{2})$ are the points which the line passes through.

So, in your case the slope is
$a=\frac{f(-1)- f(2)}{-1-2}=\frac{4- 3}{-1-2}=\frac{1}{-3}=-\frac{1}{3}$

Therefore the function can be written as
$f(x)= -\frac{1}{3} x+b$

$f(2)=3 \Rightarrow -2\frac{1}{3} +b =3 \Rightarrow b =3+\frac{2}{3}=\frac{11}{3}$

Finally the function can be written as
$f(x)= -\frac{1}{3} x+\frac{11}{3}$

So the value of $f(10)$ is
$f(10)= -10\frac{1}{3} +\frac{11}{3}=\frac{1}{3}$

Second Method
The GDC way using CASIO fx-9860 series is

MENU>STAT>Fill List1 with x-values (2 and -1) and List with the corresponding y-values (3 and 4)>CALC(F2)>REG(F3)>X(F1)> the output is

a=-0.3333333, b=3.666666.

Then you can graph the linear function y=-0.3333333x+3.666666

MENU>GRAPH>Y1=-0.3333333x+3.666666>DRAW(F6)>F5>Y-CAL>X=10 and the result is Y=0.333333

hope these help!!
miranda

Posts: 268
Joined: Mon Jan 28, 2013 8:03 pm