Question

PLS HELP!!

which equation below could represent the data in the table?

Answer 1

Answer: y = 2x+3 (choice C)

=========================================================

Step-by-step explanation:

Each time x goes up by 1, y goes up by 2.

This gives a slope of rise/run = 2/1 = 2.

Another way to get the slope is to pick two rows from the table. I'll pick the bottom two rows (1,5) and (2,7).

Use the slope formula on those points.

`(x_1,y_1) = (1,5) \text{ and } (x_2,y_2) = (2,7)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_(2) - \text{y}_(1)}{\text{x}_(2) - \text{x}_(1)}\\\\m = (7 - 5)/(2 - 1)\\\\m = (2)/(1)\\\\m = 2\\\\`

The slope is m = 2

The y-intercept is b = 3 because of the row x = 0, y = 3.

The y-intercept always happens when x = 0. It's where the graph crosses the y axis.

Plug m = 2 and b = 3 into y = mx+b to get the final answer y = 2x+3

As a check, let's plug in x = 2

y = 2x+3

y = 2*2+3

y = 4+3

y = 7

We see that the input x = 2 from the domain leads to y = 7 in the range. This matches with the last row in the table.

I'll let you check the other rows.

GeoGebra or Desmos can be used to graph and verify the answer is correct.