Question

Which equation represents a line that intersects y=1/4 x-3 at exactly one point?

a. Y=4x-3


b. Y=1/4x


c. Y-1/4x=-3


d. -2x+8y=-24

Answer 1

a. Y=4x-3

The given line, y=1/4x-3, has a slope of 1/4. For another line to intersect it at exactly one point, it must have a different slope. Among the given options, only option a, Y=4x-3, has a slope (4) that is different from the given line's slope. Therefore, it's the line that will intersect y=1/4x-3 at exactly one point.