Question

Create a graph showing the equations y equals 1 fourth invisible times x and y equals 1 fourth invisible times x minus 5. Explain how the graphs are the same and how they are different.

Answer 1

The similarity is that both equations have the same slope 1/4

The difference is that the second equation is vertically shifted downward by 5 units this makes the y-intercept of the second equation to be (0, -5), while the first equation passes through the origin.

Features of the graph

Graphing y =1/4 x

This equation represents a line with a slope of 1/4 and passes through the origin (0, 0).

Graphing y = 1/4 x - 5

This equation is similar to the first but has a vertical shift downwards by 5 units. The slope remains 1/4, but the line crosses the y-axis at (0, -5).