Question

• Write the equation of the line represented by each table. I 0 17 3 6 6 5 9 9

Answer 1

For the first table

Let's pick 2 points

x₁ = 0 y₁= 17

x₂ = 3 y₂ = 11

To form the equation, we will use the formula;

$y-y_1=\text{ }\frac{y_2-y_1}{x_2-x_1}=(x-x_1)$

substitute the values into the formula;

$y-17=\frac{11-17}{3-0}(x-0)$

Evaluate

$y-\text{ 17 =}\frac{-6}{3}(x-0)$

y - 17 = -2x

add 17 to both-side of the equation

y= -2x + 17

The above is the equation of the line for the first table

Fo the second table

Let's also pick 2 points

x₁ = 3 y₁= -2

x₂ = 6 y₂ = -4

Substitute into the formula;

$y\text{ - (-2) =}\frac{-4+2}{6-3}(x-3)$

Evaluate

$y\text{ + 2 =}\frac{-2}{3}(x\text{ - 3)}$$y\text{ + 2=-}\frac{2}{3}x\text{ + 2}$

subtract 2 from both-side of the equation

$y=-\frac{2}{3}x$

The above is the equation for table 2