Question

Consider the line y=3/4x +3. Find the equation of the line that is parallel to this line and passed through the point (-8, 6)

Answer 1

The slopes of two lines parallel to each other is equal. The equation given is

`\begin{gathered} y=(3)/(4)x+3 \\ \text{The slope is the coefficient of x.} \\ \text{That means the slope of the parallel line is }(3)/(4) \\ \text{If the other line passes through the point (-8, 6), then} \\ U\sin g\text{ the known values which are x, y and m, the other line becomes} \\ y=mx+b \\ 6=(3)/(4)(-8)+b \\ 6=-6+b \\ 6+6=b \\ b=12 \\ \text{Having known the values of m and b, the parallel line is now shown as;} \\ y=(3)/(4)x+12 \end{gathered}`

The equation of the parallel line is derived as

y = 3/4x + 12