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

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

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

$y-40=\dfrac{60-40}{50-20}(x-20)$

$y-40=\dfrac{20}{30}(x-20)$

$y-40=\dfrac{2}{3}(x-20)$

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 $-2x+3y=80$.