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Chapter 2: Q23. (page 86)

Which line best fits the data in the graph at the right?

A)鈥夆赌夆赌夆赌�y=xB)鈥夆赌夆赌夆赌�y=鈭�0.5x+4C)鈥夆赌夆赌夆赌�y=鈭�0.5x鈭�4D)鈥夆赌夆赌夆赌�y=0.5+0.5x

Short Answer

Expert verified

The correct option is D)鈥�鈥�鈥�鈥�0.5+0.5x.

Step by step solution

01

Step-1 – Determine the points.

The coordinates of the points are (1,0.5),(2,1.5),(3,2),(4,2.5)

02

Step-2 – Calculate the slope of the line.

The slope is positive so all options with negative slope must be incorrect.

Take any two points and determine the equation except the points (1,0.5).

Let the points are (2,1.5)鈥�鈥�鈥�and鈥�鈥�(3,2)鈥�.

Substitute (x1y1)=(2,1.5)鈥�鈥�鈥�and鈥�鈥�(x2y2)=鈥�(3,2)into the formula slope=y2-y1x2-x1

m=2鈭�1.53鈭�2m=0.5

03

Step-3 – Make the equation.

Substitute (x1y1)=(2,1.5)鈥�into y-y1=m(x-x1).

localid="1647259272468" y鈭�1.5=0.5(x鈭�2)y鈭�1.5=0.5x鈭�1y=0.5x+0.5

From the given options the only possible match can be option D)鈥�鈥�鈥�鈥�0.5+0.5x.

Thus, the line best fits the data in the graph should be D)鈥�鈥�鈥�鈥�0.5+0.5x.

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