Question

Find an equation for the family of linear functions with slope 2 and sketch several members of the family

Answer 1

 f(x)=2x+b. the general eqtn is y=2x+b where b can be +ve or -ve. If you draw y = 2x, you get a line of slope 2, passing through the origin. The line y = 2x+3 is parallel to y = 2x, and cuts the y-axis at y = 3. Similarly, the line y = 2x-1 is parallel to y = 2x, and cuts the y-axis at y = -1. You do not need any points to sketch them on our graph: the lines you draw must just be parallel to y = 2x