Solution assignment 10 Linear functions and graphs

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Assignment 10

The line l goes through the points P(1,2) and Q(-1,-1). For which value of r is the line:

m: y=rx-3

parallel to l?

Solution

Parallel lines have equal slopes. The slope of l is:

\displaystyle\frac{y_Q-y_P}{x_Q-x_P}=\displaystyle\frac{-1-2}{-1-1}=\displaystyle\frac{-3}{-2}=\displaystyle\frac{3}{2}

The equation of l is:

y-2=\displaystyle\frac{3}{2}(x-1)
y=\displaystyle\frac{3}{2}x+\displaystyle\frac{1}{2}

The line l is parallel to m if:

r=\displaystyle\frac{3}{2} and \displaystyle\frac{1}{2}\neq-3

Both conditions are satisfied and thus the line l is parallel to m and does not coincide with it.

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