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Answer 1 · 2017-06-25T00:43:42

See below.

The x-intercept is defined to be the point at which the line intersects the x-axis. You can calculate it by substituting $y=0$ into the equation:

$y=1/4x+1$

$0=1/4x+1$

$-1=1/4x$

$(-1)(4)=(1/4)x(4)$

On the right-hand side of the equation the $4$ 's cancel since one is in the numerator and the other is in the denominator.

$x=-4$

So the x-intercept is $(-4,0)$

The y-intercept is defined to be the point at which the line intersects the y-axis. You can calculate it by substituting $x=0$ into the equation:

$y=1/4x+1$

$y=1$

The y-intercept is $(0,1)$

Here's what the graph looks like:

graph{1/4x+1 [-10, 10, -5, 5]}