Q18.

Graph each inequality.

18. . $y - 2 < 3 x$

Verified

Answer

The graph of the inequality is shown below:

1Step 1 – Find the boundary line equation of the given equation.

Consider the inequality $y - 2 < 3 x$

The boundary line equaton is $y - 2 = 3 x$

Here the inequality is $<$ , graph the boundary line as a dashed line.

Find the slope intercept form of $y - 2 = 3 x$

$\begin{array}{l} y - 2 = 3 x \\ y = 3 x + 2 add 2 on both sides \end{array}$

The equation $y = 3 x + 2$ is in slope intercept form with slope 3

2Step 2 – Choose a test point and test the inequality.

Choose the test point as $(0, 0) .$

Substitute $x = 0, y = 0$ in $y - 2 < 3 x$

$\begin{array}{l} y - 2 < 3 x \\ 0 - 2 < 3 (0) substitute 0 for x, 0 for y \\ - 2 < 0 true \end{array}$

3Step 3 – Conclusion

Since, $- 2 < 0$ results a true inequality, so, shade the region that contains the point $(0, 0) .$

Graphical representation of $y - 2 < 3 x$

Q17.