Question

Observe the graph:


Observe the table:

Input	1	4
Output	A	150

Find the missing value and find the equation for the table if the slope of the graph and table is same.

• A. A = 45, y = 35x + 10
• B. A = 45, y = 30x + 10
• C. A = 45, y = -30x + 10
• D. A = 45, y = -35x + 10

Answer 1

The correct option is A A = 45, y = 35x + 10

From the graph consider any two points say, (1,75) and (2,110)


$\text{Slope}=\frac{\text{Change in y}}{\text{Change in x}}=\frac{110-75}{2-1}=35$

Given that slope of graph is equal to slope of table = 35

Input	1	4
Output	A	150

So,
$\text{Slope of the table}=\frac{\text{Change in y}}{\text{Change in x}}=\frac{150-A}{4-1}=35$

$\Rightarrow 150-A=35\times 3$

$\Rightarrow 150-A=105$

$\Rightarrow 150-105=A$

$\Rightarrow A=45$

Representing the value in the table, we observe:

Input	1	4
Output	45	150

Equation for the point slope form:

$y-y_1=m(x-x_1)$

Putting (1,45) in the equation, we get:

$\Rightarrow y-45=35(x-1)$

$\Rightarrow y-45=35x-35$

$\Rightarrow y=35x+10$

Therefore, the equation for the table is $y=35x+10.$