A scatter plot with a trend line is shown below. Which equation best represents the given data?

Solution:

The equation can be found using the slope intercept form

y = mx + b

Where m is the slope of the line

b is the y intercept

By using the points (2,5) and (8, 9) from the scatter-plot

m = (y₂ - y₁)/ (x₂ - x₁)

Substituting the values

m = (9 - 5) / (8 - 2)

m = 4/6 = 2/3

Thus m = 2/3

Substituting it in the formula using the point (2, 5)

5 = 2/3 × 2 + b

5 = 4/3 + b

b = 5- 4/3

b = 11/3

Therefore, the equation is y = 2/3x + 11/3

⇒3y = 2x +11.

A scatter plot with a trend line is shown below. Which equation best represents the given data?

Summary:

A scatter plot with a trend line is shown. The equation which best represents the given data is 3y = 2x +11.