Question

Write the equation of the line that connects the set of data points!helppp

Answer 1

Given:

The set of data points on the graph.

To find:

The equation of line that connects the set of data points.

Solution:

From the given graph it is clear that the data points are (20,40), (35,50), (50,60), (65,70).

If a line passes through two points
`(x_1,y_1)` and
`(x_2,y_2)`, then the equation of line is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

Let as consider the line passes through (20,40) and (50,60), then the equation of line is

`y-40=(60-40)/(50-20)(x-20)`

`y-40=(20)/(30)(x-20)`

`y-40=(2)/(3)(x-20)`

Multiply both sides by 3.

`3(y-40)=2(x-20)`

`3y-120=2x-40`

Isolate variable terms.

`-2x+3y=120-40`

`-2x+3y=80`

Therefore, the standard form of the required line is
`-2x+3y=80`.