Question

Fill in the table so it represents a linear function.

Answer 1

Answer:

2; 5; 8

Step-by-step explanation:

To fill in the table, we need to generate an equation to represent the relationship between x and y.

First, find the slope using the two pairs given, (5, -1) and (25, 11):

$slope (m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{11 -(-1)}{25 - 5} = \frac{12}{20} = \frac{3}{5}$

m = ⅗.

Next, using the point-slope form, we can use a point/coordinate pair and the slope to derive an equation as follows.

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

Where,

$x_1 = 5, y_1 = -1$

m = ⅗.

Plug in the values

$y -(-1) = \frac{3}{5}(x - 5)$

$y + 1 = \frac{3}{5}(x - 5)$

$y + 1 = \frac{3x}{5} - 3$

Subtract 1 from both sides

$y + 1 - 1 = \frac{3x}{5} - 3 - 1$

$y = \frac{3x}{5} - 4$

Use the equation above to fill out the table by plugging each value of x into the equation to get the corresponding values of y for each x value.

✔️When x = 10:

$y = \frac{3x}{5} - 4$

$y = \frac{3(10)}{5} - 4 = 6 - 4$

$y = 2$

✔️When x = 15:

$y = \frac{3x}{5} - 4$

$y = \frac{3(15)}{5} - 4 = 9 - 4$

$y = 5$

✔️When x = 20:

$y = \frac{3x}{5} - 4$

$y = \frac{3(20)}{5} - 4 = 12 - 4$

$y = 8$