Question

Write and graph an equation in two variables that shows the relationship between the time and the distance.

Moves 15 meters in 1 second.

Answer 1

The relation between the time and the distance will be:

y = 15x

The graph of the equation y = 15x is attached below.

Explanation:

We know that the equation of linear function in two variables in the slope-intercept form is

y = mx+b

where

• m is the rate of change or slope

• b is the y-intercept

Let y be the distance

Let t be the time

Given that the object moves 15 meters in 1 second.

Thus, the rate of change or slope = m = 15

As there is no initial condition in our case.

Thus the y-intercept b = 0

Now, substituting m = 15 and b = 0 in the linear function

y = mx+b

y = 15x + 0

y = 15x

Therefore, the relation between the time and the distance will be:

y = 15x

The graph of the equation y = 15x is attached below.

Examples:

Calculate the distance in 1 second

put x = 1 in the equation

y = 15(1) = 15 meters

Calculate the distance in 10 second

put x = 10 in the equation

y = 15(10) = 150 meters