The equation -4x + y = 0 relates the number of pages in a photo album y to the number of pictures in the album x. How do you tell whether the relationship is a direct variation?

Question

The equation  -4x + y = 0  relates the number of pages in a photo album y to the number of pictures in the album x. How do you tell whether the relationship is a direct variation?

Kennedy Adams · Accepted Answer

The y-intercept of the equation is #0#.

Recall the general equation for a line in slope-intercept form: #y=mx+b# where: #y=#y-coordinate #m=#slope #x=#x-coordinate #b=#y-intercept In this equation, if you isolate for #y#, you end up with an equation that looks like this: #-4x+y=0# #-4x# #color(red)(+4x)+y=0# #color(red)(+4x)# #rArry=4x# #color(blue)(+0)# Recall that in direct variation, the graph goes through the origin, #(0,0)#. Since the y-intercept of this equation is #color(blue)0#, this means the graph intersects the origin. Thus, this graph represents direct variation. If you were to graph the line, you would see the intersection at #(0,0)#: graph{y=4x [-12.66, 12.65, -6.33, 6.33]}

Eva Abramson · Answer

undefined To determine if the relationship is a direct variation, you need to check if the equation can be written in the form y = kx, where k is a constant. In this case, the equation -4x + y = 0 can be rearranged to y = 4x, indicating a direct variation relationship since y is directly proportional to x with a constant of 4. Therefore, the relationship is a direct variation.