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A function $f(x)$ is linear and has a value of $29$ at $x=-2$ and $39$ at $x=3$. Find its value at $x=5$.

1. $59$
2. $45$
3. $43$
4. $35$

$f(x)$ is linear means it is of the form $ax+b$

given $f(-2)$ and $f(3)$

solve the equation and find out value for $a$ and $b$ then find $f(5)$. it will be $43$

Correct Answer: $C$

### 1 comment

-2a + b = 29

3a + b = 39

therefore , -5a = -10  , a = 2  & b= 33

f(5) = 5*a + b = 5*2 + 33 = 10 + 33 = 43 .

yup , that's correct .

Here, $f(x)$ is linear. It means that $f(x)$ represents a straight line. So $(-2,29)$ and $(3,39)$ are the two points on this line.
Therefore, the equation of the line is $$y-29=\left(\frac{39-29}{3-(-2)}\right)\left (x-(-2) \right)$$

[As we know $y-y_1=m(x-x_1)$ where $m$ is the slope and $m=\frac{y_2-y_1}{x_2-x_1}$]

$$\Rightarrow y=2(x+2)+29=2x+33\\ \therefore f(x)=2x+33$$

So at $x =5$,  $f(5)=2(5)+33=43$.

equation for linear function f(x)=ax+b

f(-2)= -2a+b =29                            ………..(1)

f(3) = 3a+b = 39                            ………...(2)

subtracting eq(1) from eq(2)

5a=10

a=2  and b=33

f(5)=5a+b = 10+33=43

### 1 comment

Plot given values in a graph it will make a straight line having coordinates (-2,29) &(3,39) now use (y-y1)=(y2-y1)/(x2-x1)*(x-x1)

Use X =5 and find y=43✌️