Question

Graph: y - 4x >= - 1 then shade in the side that satisfies the inequality.

Answer 1

The given inequality is:

`y-4x\ge-1`

To graph it, first, let's find the equation of the line in slope-intercept form:

`\begin{gathered} y-4x=-1 \\ \text{ Add 4x to both sides} \\ y-4x+4x=4x-1 \\ y=4x-1 \end{gathered}`

The slope is 4 and the y-intercept is -1.

So, starting at y=-1 and x=0, we move 4 units up and 1 unit to the right to find the next point on the graph.

It will be located at (1,3).

By joining these two points, we can graph the line of the inequality:

Now, as the inequality says y values greater than or equal to this line, then the side that satisfy the inequality is the side above the line: