Mathematics, 22.11.2020 08:20 annalee15

A number of squares are connected in a row to form a rectangle. The table shows the relationship between the number of squares, x, and the perimeter, y, of the rectangles they form
Select all the true statements about this relation.

A number of squares are connected in a row to form a rectangle. The table shows the relationship be

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Answer from: samstuart10p3g96w

The true statements are:

(a) The equation of the function is $\mathbf{y = 4x +4}$ (c) The relation is a function(e) The graph is linear

(a) The equation of the function

Start by calculating the slope (m)

$\mathbf{m = \frac{y_2 - y_1}{x_2 -x_1}}$

So, we have:

$\mathbf{m = \frac{12 - 8}{2 -1}}$

$\mathbf{m = 4}$

The equation is then calculated as:

$\mathbf{y = m(x -x_1) + y_1}$

So, we have:

$\mathbf{y = 4(x -1) + 8}$

$\mathbf{y = 4x -4 + 8}$

$\mathbf{y = 4x +4}$

Hence, this statement is true

(b) The graph is nonlinear

Because of (a) above, the graph is linear

Hence, this statement is false

A linear relation is a function

Hence, this statement is true

(d) The rate of change is not constant

Because of (a) above, the rate of change is constant

Hence, this statement is false

(e) The graph is linear

Because of (a) above, the graph is linear

Hence, this statement is true

Read more about linear relations at:

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Answer from: lilybear1700

✅The table can be represented by the equation, y = 4x + 4

✅The relation is a function.

✅The graph of the function is linear.

Step-by-step explanation:

✍️The first statement: The table can be represented by the equation, y = 4x + 4 .

To check if the first statement is correct let's find the equation that can represent the table by finding the slope (m) and y-intercept (b).

Using two pairs, (1, 8) and (2, 12),

Slope = $\frac{y_2 - y_1}{x_2 - x_1} = \frac{12 - 8}{2 - 1} = \frac{4}{1} = 4$ .

Substitute, x = 1, y = 8, and m = 4 into y = mx + b to solve for b.

Thus:

8 = (4)(1) + b

8 = 4 + b

Subtract 4 from each side

8 - 4 = b

4 = b

Plug in the values of b and m into y = mx + b.

Thus, the equation that represents the table would be:

y = 4x + 4 .

✅Therefore, the first statement is correct.

✍️The second statement: The graph of the function is non-linear.

This is NOT TRUE because the equation of the function, y = 4x + 4 , represents the equation of a linear graph in the slope-intercept form. When graphed, it will give us a straight line.

✍️The Third statement: The relation is a function.

This is TRUE because each input value (x-value) has exactly one output value (y-value).

✍️The Fourth statement: The rate of change is NOT constant.

This standby is NOT TRUE.

The rate of change is the slope (m) that we have calculated above to be 4. Between any two pairs, the rate of change remains 4.

Therefore, this statement is not correct.

✍️The Fifth statement: The graph of the function is linear.

This is TRUE. As stated earlier, from the equation generated, it is safe to say that the equation represents graph of a linear function. The graph will be a straight line graph.

Answer from: Quest

you need more information to answer this question

step-by-step explanation:

Answer from: Quest

answer: a.

step-by-step explanation: the answer is a. because, you need to converge the fractions to find a solution.