Question

A line In the xy-plane that passes through the coordinate points (3,-6) and (-7,-4)will never intersect a line that is represented by which of the following A. X + 5y=6B. X + y/2=7C.2y-x=-8

Answer 1

As a first step we can calculate the slope of the line that passes through the points given:

(3, -6) and (-7, -4)

Slope is given by the expression:

$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-4-(-6)}{-7-3} \\ m=\frac{2}{-10}=-\frac{1}{5} \end{gathered}$

Now, we can find the equation of the line by the slope-point form of a line:

$\begin{gathered} y-y_0=m(x-x_0) \\ y+6=-\frac{1}{5}(x-3) \\ y=-\frac{1}{5}x+\frac{3}{5}-6 \\ y=-\frac{1}{5}x-\frac{27}{5} \end{gathered}$

Lines will never intersect if they have the same slope.

A. x+5y=6

5y=6-x

y=-1/5x+6/5 ---> A has the same slope as the other line