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Maths-

General

Easy

Question

For the linear function f, the graph of y = f(x) in the xy -plane passes through the points (0, 2) and (2, 6). Which equation defines f ?

$y = \frac{1}{2} x + 2$
$y = \frac{2}{3} x + 2$
$y = 2 x + 2$
$y = 3 x + 2$

The correct answer is: $y equals 2 x plus 2$

If a graph of a linear function $y equals f open parentheses x close parentheses$ passes through some points $left parenthesis x subscript 1 end subscript comma y subscript 1 end subscript right parenthesis$ , $open parentheses x subscript 2 end subscript comma y subscript 2 end subscript close parentheses$ then the function of the graph must satisfy with the points, viz. $y subscript 1 end subscript equals f open parentheses x subscript 1 end subscript close parentheses$ and so on.
Explanations:
Step 1 of 3:
For the linear function $f$ , the graph of $y equals f open parentheses x close parentheses$ in the $x y$ -plane passes through the points $open parentheses 02 close parentheses blank$ and $open parentheses 26 close parentheses$ .
Consider the equation given in option C, $y equals 2 x plus 2$ .
Step 2 of 3:
Now, putting $x equals 0$ , we get $y equals open parentheses 2 cross times 0 close parentheses plus 2 equals 2$
Thus, $open parentheses 02 close parentheses$ satisfies the equation $y equals 2 x plus 2$ .
Step 3 of 3:
Now, putting $x equals 2$ , we get $y equals open parentheses 2 cross times 2 close parentheses plus 2 equals 4 plus 2 equals 6$
Thus, $open parentheses 26 close parentheses$ also satisfies the equation $y equals 2 x plus 2$ .
So, $open parentheses 02 close parentheses$ and $open parentheses 26 close parentheses$ both satisfy the equation $y equals 2 x plus 2$ .
Final Answer:
The equation defines $f$ — y = 2x + 2 .

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