Answer:
True
Step-by-step explanation:
To see if the points all lie on the line y = 4/3x + 5, substitute their x and y values into the equation, solve, and see if the equation is true.
1) First, substitute the x and y values of (6,13) for the x and y in the equation and solve:
[tex]13 = \frac{4}{3} (6) + 5 \\13 = \frac{24}{3} +\frac{15}{3} \\13 = \frac{39}{3}\\13 = 13[/tex]
The result is a true equation. Thus, (6,13) is on the line.
2) Do the same with the point (21,33):
[tex]33 = \frac{4}{3} (21) + 5 \\33 = \frac{84}{3} +\frac{15}{3} \\33 = \frac{99}{3} \\33 = 33[/tex]
The result is a true equation. Thus, (21,33) is on the line.
3) Finally, do the same with (99, 137):
[tex]137 = \frac{4}{3} (99) + 5\\137 = \frac{396}{3}+\frac{15}{3} \\137 = \frac{411}{3} \\137 = 137[/tex]
The result is a true equation. Thus, (99, 137).
All three points are on the line, thus the statement is true.
