Question

Luz drives at an average speed of 45 miles per hour. She has driven for 3 hours and has travelled a distance of 135 miles. This situation can be represented with a linear equation written in point-slope form, where x represents the number of hours and y represents the number of miles. Use this information to complete each statement about the linear equation.

Answer 1

The slope of the linear equation is 45.

A point on the graph of a linear equation will be (3, 135).

This linear equation can be written as (y-135)=45(x-3).

Answer 2

`(y-135)=45(x-3)`

Step-by-step explanation:

Let x represents the number of hours and y represents the number of miles.

We are told that Luz drives at an average speed of 45 miles per hour. She has driven for 3 hours and has traveled a distance of 135 miles.

We can see from our given information that slope of line is 45 as with each increase in number of hours (x), change in distance (y) is 45.

`m=(y_2-y_1)/(x_2-x_1)`

`m=(135-0)/(3-0)`

`m=(135)/(3)`

`m=45`

Since the equation of line in point-slope form is :
`(y-y_1)=m(x-x_1)`, where m represents slope of line and
`(y_1,x_1)` represents a point the line passes through.

Upon substituting our given values in point-slope form of equation we will get,

`(y-135)=45(x-3)`

Therefore, the equation represented in point-slope form will be:
`(y-135)=45(x-3)`.