The given table shows a linear relationship between the total number of wooden legs and the chairs in a dining table set

If a particular dining table set has 12 chairs, then how many legs will this set have?

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Solution

The correct option is C 52
Given:
The table shows a linear relationship between the total number of wooden legs and the chairs. Let’s first construct the equation in the slope-intercept form, and then solve the equation by substituting the number of chairs to be 12.

To find the equation in the slope-intercept form $(y = m x + b)$ , let’s first find the slope by considering the following two points: (2, 12) and (3, 16)
Slope $m = \frac{Change in y}{Change in x} = \frac{16 - 12}{3 - 2} = \frac{4}{1} = 4$
Slope m = 4 .
$\to$ Equation: $y = 4 x + b$
Now, let’s substitute the point (2, 12) in the equation to get the y-intercept.
$12 = 4 (2) + b$
$\Rightarrow 12 = 8 + b$
$\Rightarrow b = 4$
Therefore, the equation of the line is: $y = 4 x + 4$
Now, the question asks what will be the number of legs (y) if the number of chairs (x) are12.
So, $x = 12$
$\Rightarrow y = 4 (12) + 4 = 48 + 4 = 52$
$\to$ Option C is correct.

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The given table shows a linear relationship between the total number of wooden legs and the chairs in a dining table set If a particular dining table set has 12 chairs, then how many legs will this set have?

The given table shows a linear relationship between the total number of wooden legs and the chairs in a dining table set

If a particular dining table set has 12 chairs, then how many legs will this set have?