Algebra one graphing families?

Question

Are the following two graphs in a family? If so, explain why.

y = -2x + 3 and y = 2x + 3

Answer 1

Hi,

While both of these are linear equations that graph as straight lines, families of graphs are usually things that have the same shape as each other. In the case of linear equations, families will have the same slope but different y intercepts. That way the entire family looks alike because they are all parallel lines with different y intercepts.

Equations like yours are not a family just because they have the same y intercept. I could have a graph shaped like a W that has a y intercept of 3, but it clearly doesn't have the same shape or the same slope.

Equations of parabolas that have the exact same shape but are shifted or transformed to other positions would also be an example of a family of equations. So y = x² and y = (x - 3)² and y = (x + 4)² - 6 would be in a family because their curves could be picked up off the paper and slid to another graph's position, they would match perfectly.

So, y = -2x + 3 and y = -2x + 8 and y = -2x - 1 are in a family with the slope of -2. Your equations are NOT in a family.

I hope this helps!! :-)

Answer 2

Yes . They have same y-intercept.
This is the family of straight lines that have different slopes, but the same y-intercept =3.