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?

Answer 1

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

Explanation:

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]}