Question

17. Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.
Show your work.

`y = 1/4x + 10`
`-2x + 8y = 6`

Answer 1

To determine whether the lines are parallel, perpendicular, or neither, we need to examine their slopes.

For the first equation, `y = 1/4x + 10`, it is in slope-intercept form, y = mx + b, where m represents the slope. So the slope of the first equation is 1/4.

For the second equation, -2x + 8y = 6, we need to rewrite it in slope-intercept form. Starting with -2x + 8y = 6:
8y = 2x + 6 (we added 2x to both sides)
y = 1/4x + 3/4 (we divided both sides by 8)

Now, we can see that the slope of the second equation is also 1/4.

Since both lines have the same slope of 1/4, the lines are parallel.