Question

The given table gives the information time (in days) and value of sales (in $). Find the missing term to make it a linear function.

• A. 163
• B. 203
• C. 253
• D. 193

Answer 1

The correct option is A 163

Given

x: Time (in days)	y: Value of sales (in $)
1	43
3	83
5	123

Consider any two coordinates, say (1,43) and (3,83)

$\text{Slope}=\frac{\text{Change in y}}{\text{Change in x}}=\frac{83-43}{3-1}$

$\text{Slope = 20}$

Equation of straight line is y = mx + c

Putting the value of m, we get:
$y=20x+c$

Consider one point, let say (5,123)

Substituting the values, we get:

$\Rightarrow 123=20\left(5\right)+c$

$\Rightarrow 123=100+c$

$\Rightarrow 23=c$

Therefore, the equation for the above table will be y = 20x + 23

At x = 7,
$y=20\times 7+23=140+23=163$

Therefore, in 7 days, the sales will be $\$$163.

So, the complete table can be represented as:

x: Time (in days)	y: Value of sales (in $\$$)
1	43
3	83
5	123
7	163