Question

Without graphing, determine whether the following pair of lines are parallel, perpendicular, or neither parallel nor perpendicular

Answer 1

Write the equation of the lines in slope-intercept form (y=mx+b)

First equation: It is already in slope-intercept form

$y=\frac{2}{5}x-4$

Second equation: solve y:

$\begin{gathered} 4x-10y=-7 \\ 4x-4x-10y=-4x-7 \\ -10y=-4x-7 \\ \frac{-10}{-10}y=\frac{-4}{-10}x-\frac{7}{-10} \\ \\ y=\frac{4}{10}x+\frac{7}{10} \\ \\ y=\frac{2}{5}x+\frac{7}{10} \end{gathered}$

Identify the slope of each line:

If two or more lines have the same slope then the lines are parallel

If two lines have slopes that are negative reciprocals then the lines are perpendicular

The two given lines have the same slope: 2/5. Then, they are parallel lines