Question 20532
Hello There:

Here is the information that you need to answer these questions.

An equation of the form x = c, where c is a real number, has a graph that's a vertical line.

Your two equations x = -2 and x = 3 are vertical lines that intersect the x-axis at (-2, 0) and (3, 0).

An equation of the form y = c, where c is a real number, has a graph that's a horizontal line.

Your equation y = -7 is a horizontal line that intersects the y-axis at (0, -7)

When two lines have the same slope, they are parallel.

When two lines have slopes that are negative reciprocals of each other, they aer perpendicular.

Solving for y shows us the slope.

This equation is already solved for y:

y = 2*x - 1

Solving this equation: y/2 = x + 3 gives us:

y = 2*x + 6

Both of these lines have slope 2, so they are parallel.

Solving 2*y = -x leads to: y = -(1/2)*x

This slope is -1/2; so it's the negative reciprocal of 2 (the slope of the parallel lines).

So, 2*y = -x is the line that is perpendicular to y/2 = x + 3 and y = 2*x - 1.

~ Mark