Question

Do the points on the linehave a constant ratio of they-coordinate to the x-co-ordinate for any point onthe line except the y-inter-cept? Explain your answer.

Answer 1

$\begin{gathered} \text{the ratio asked is} \\ m=\frac{y}{x},\text{ which is the slope by taking the initial point as the origin} \\ when\text{ the line intercept the y axes, x =0} \\ \text{then } \\ m=\frac{y}{0} \\ \sin ce\text{ its a dividision by zero, the slope is infinite} \\ \end{gathered}$$\begin{gathered} \text{remember that the slope, in general, is given by} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ \text{where, point A could be A=(x}_1,y_1)andpointBcouldbeB=(x_2,y_2) \end{gathered}$$\begin{gathered} \text{if you take as point A=(0,0), the slope equation is} \\ m=\frac{y_2}{x_2} \end{gathered}$