A set of data is represented by the scatter point in the portion of the xy-plane shown. Which of the following linear equations best fits the data?

The correct answer is: y = 15.2 + 16x

Looking at the scatter point, we are given various points that lie on the equation that we need to find.
Also, we can find the slope of the said equation by using the formula-

Then, we can find the equation by using point- slope formula i.e.
y - y₁ = m (x - x^₁)
Step-by-step solution:-
In the given diagram, we find the slope by taking any 2 points on the graph to calculate the difference between them. We take Points A (5.2, 95) & B (6.8, 123)
Here, x₁ = 5.2, y₁ = 95; x₂ = 6.8 & y₂ = 123
Slope =


∴ m = 17.5
In the given Options, the equation in the form y = mx + c (y = c + mx here), the value of m that is closest to our calculation is 16.
∴ m = 16 __________________________-- (Equation i)
∴ Options A & B are eliminated.
Now, calculating the equation by Point-clope formula, taking Point A (5.2,95) and slope = m = 16, we get-
y - y1 = m (x - x1)
∴ y - 95 = 16 (x - 5.2)
∴ y - 95 = 16x - 83.2
∴ y = 16x - 83.2 + 95
∴ y = 16x + 11.8
In the remaining options C & D, the equation that has the value of c closest to our calculation is Option D i.e. 15.2.
Final Answer:-
Option D i.e. y = 15.2 + 16x is the correct Option.
Note:-
In the given scatter diagram, we have been provided with a section of the whole diagram and hence, the origin (0,0) is not visible in this section. Also, this leads to the minor variation in the values of slope that we get in our calculation.