Question

which graph best represents the solution set of $y > 3x - 4$? (four graphs labeled a, b, c, d are shown, with a and c having shaded regions on one side of a line, b and d on the other; a and b have solid lines, c and d have dashed lines)

Explanation:

Step1: Determine the type of line

For the inequality \(y>3x - 4\), since the inequality is strict (\(>\)), the boundary line \(y = 3x-4\) should be a dashed line.

Step2: Determine the shaded region

We can use a test - point. Let's take the point \((0,0)\).
Substitute \(x = 0\) and \(y = 0\) into the inequality \(y>3x - 4\):
\(0>3\times0 - 4\), which simplifies to \(0>-4\) (a True statement).
So, the region that contains the point \((0,0)\) should be shaded.

Answer:

C