Question

true or false:the points (6,13),(21,33),(99,137)all lie on the-same line. the equation of the line is y=4/3x +5

Answer 1

The answer is true.

Step-by-step explanation:

To find the points all lie on the same line, we need to substitute the points in the equation of the line, to determine if the values on both sides of the equation are equal.

Substituting the point $(6,13)$ in the equation of the line, we get,

$\begin{aligned}y &=\frac{4}{3} x+5 \\13 &=\frac{4}{3}(6)+5 \\&=4(2)+5 \\&=8+5 \\13 &=13\end{aligned}$

Thus, the values on both sides are equal. The point $(6,13)$ lie on the same line.

Substituting the point $(21,33)$ in the equation of the line, we get,

$\begin{aligned}y &=\frac{4}{3} x+5 \\33 &=\frac{4}{3}(21)+5 \\&=4(7)+5 \\&=28+5 \\33 &=33\end{aligned}$

Thus, the values on both sides are equal. The point $(21,33)$ lie on the same line.

Substituting the point $(99,137)$ in the equation of the line, we get,

$\begin{aligned}y &=\frac{4}{3} x+5 \\137 &=\frac{4}{3}(99)+5 \\&=4(33)+5 \\&=132+5 \\137 &=137\end{aligned}$

Thus, the values on both sides are equal. The point $(99,137)$ lie on the same line.

Thus, all the three points lie on the same plane.

Hence, the answer is true.