Question

Consider the line -4×-2y=-6what is the slope of a line parallel to this line?what is the slope of a line perpendicular to this line?

Answer 1

The general equation of a line is y=mx+c, where m is the slope and c is the y intercept.

Transform the equation of line -4x-2y=-6 into the general form.

`\begin{gathered} -4x-2y=-6 \\ -2y=-6+4x \\ y=(-1)/(2)(-6+4x) \\ y=3-2x \\ y=-2x+3 \end{gathered}`

Compare equation y=-2x+3 with y=mx+c. Then, we get

Slope, m=-2.

The slope of two parallel lines are equal. Therefore, the slope of a line parallel to -4x-2y=-6 is -2.

If m is the slope of line, then the slope of a line perpendicular to it is -1/m. Therefore, the slope of perpendicular line can be calculated as

`\text{slope}=-(1)/(m)=-(1)/((-2))=(1)/(2)`

Hence, the slope of perpendicular line is 1/2.