Question

Line m passes through the points (-4, 3) and (-4, 7). What is the slope of the line that is parallel to line m?

Answer 1

Gradient=rise/run=y2-y1/x2-x1

= 7-3(4)/-4--4(0)

As you can't divide by zero the line's equation is x=-4 so it doesn't have a gradient as such. However, a parallel line would be the y-axis

Answer 2

S = (y2-y1) / (x2-x1)
S = (7 - 3) / (-4 - -4)
S = 4 / 0
S = 0

or you can just note how both x points are the same, so it must be a straight, vertical line

if both x points are the same, it's a vertical line that passes through (that point, 0)

if both y points are the same, it's a horizontal line that passes through (0, that point)

the slope of a line that's parallel to either is going to have the same slope because they will never intersect, therefore proving that they never bend or are at different angles