the functions in order from least to greatest rate of change.
[tex]y=\frac{1}{2}x-2\\y=\frac{3}{4}x-10 \\y=\frac{3}{2}x+\frac{11}{2}\\y=\frac{5}{2}x+10\\[/tex]
Rate of change:
Slope of a line is the rate of change. Slope of a line tells us the steepness of the line. Equation of a line of the form y=mx+b
where m is the slope that is the rate of change.
Find the rate of change from each equation
[tex]y=\frac{3}{4}x-10\\slope =\frac{3}{4}\\\\y=\frac{3}{2}x+\frac{11}{2}\\slope =\frac{3}{2}\\\\y=\frac{1}{2}x-2\\slope =\frac{1}{2}\\\\y=\frac{5}{2}x+10\\slope =\frac{5}{2}\\[/tex]
Now we compare all the slopes
Slopes are the rate of change
[tex]slope =\frac{3}{4}\\ slope =\frac{3}{2}\\slope =\frac{1}{2}\\ slope =\frac{5}{2}\\\\\frac{1}{2} < \frac{3}{4} < \frac{3}{2} < \frac{5}{2}\\[/tex]
The function from least to greatest rate of change is
[tex]y=\frac{1}{2}x-2\\y=\frac{3}{4}x-10 \\y=\frac{3}{2}x+\frac{11}{2}\\y=\frac{5}{2}x+10\\[/tex]
Learn more information about rate of change here :
brainly.com/question/11546715
