Set of ordered pairs (x, y) could represent a linear function
B= {(-1,2), (2, 1), (5,0), (8, -1)}
Option B is correct
Linear Function
Linear function is a function whose graph is a straight line .
Slope
Slope of a line tells us how steep the line is . Slope of a line is same at all the points.
Slope formula is [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Lets find out slope of any two points in each option
A = {(-6,3), (-3,0), (0, -3), (3,-5)}
[tex]\frac{0-3}{-3+6} =-1\\\frac{-5+3}{3-0} =-\frac{2}{3} \\[/tex]
Slopes are not same
Lets check the second option
B={(-1,2), (2, 1), (5,0), (8, -1)}
[tex]\frac{1-2}{2+1} =\frac{-1}{3} \\\frac{0-1}{5-2} =\frac{-1}{3} \\\frac{-1-0}{8-5} =\frac{-1}{3} \\[/tex]
The slope of any two points are equal .
slope are same . So it represents a linear function .
C = {(-4,-7), (-1, -3), (2.0), (5,3)}
[tex]slope =\frac{-3+7}{-1+4}=\frac{4}{3} \\slope =\frac{0+3}{2+1}=\frac{3}{3}=1[/tex]
Slopes are not same . So it is not a linear function
D = {(-5, -8), (-2,-4), (1,1), (4,6)}
[tex]slope = \frac{-4+8}{-2+5}= \frac{4}{3} \\Slope = \frac{1+4}{1+2}= \frac{5}{3} \\\\slope = \frac{6-1}{4-1}= \frac{5}{3} \\[/tex]
Slopes are not same . so it is not a linear function .
Option B is correct.
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