Answer
Please see the graph, made using graphing software.
Work Step by Step
$y\geq1/4*x+3$
The y-intercept is $3$, and the slope is $1/4$, and we can use this to draw the line on the graph.
$(0,3)$ is on the line (as the y-intercept), and $(4,4)$ is also on the line. (The change in y-values for the slope is 1, and the change in x-values for the slope is 4.)
If we add the change in x-values from the slope to the x-value for the y-intercept, we have $4+0 = 4$.
If we add the change in y-values from the slope to the y-value for the y-intercept, we have $1 + 3 = 4$.
Thus, another point on the line is $(4,4)$.
Use $(0,0)$ as a test point to determine what side of the graph to shade.
$y\geq1/4*x+3$
$0\geq1/4*0+3$
$0 \geq 0+3$
$0 \geq 3$ is a false statement, so we shade the side of the graph without $(0,0)$.
