Question

What is the slope and intercept for `y=1/4x` and how would you graph it?

Answer 1

Slope: `1/4`
y-intercept: `0`
(see below for graph)

Explanation:

The slope-intercept form of a linear equation is
`color(white)("XXX")y=color(red)(m)x+color(blue)(b)`
`color(white)("XXXXXX")`where `color(red)(m)` is the slope and `color(blue)(b)` is the y-intercept.

`y=1/4x hArr y=color(red)(1/4)x+color(blue)(0)`

`rarr` slope `=color(red)(1/4)` and y-intercept `=0`

Since the y-intercept is `0`
the line goes through the point `(0,0)`
and substituting some multiple of `4` (e.g. `8`) for `x`we can easily determine a second point (in this case `(8,2)`)

Plot these two points on the Cartesian plane and draw a line through them for the required graph.
graph{(y-x/4)(x^2+y^2-0.01)((x-8)^2+(y-2)^2-0.01)=0 [-1.885, 13.915, -3.42, 4.48]}