Question

Graph the linear inequality y < 3x using slope-intercept form.

Answer 1

See attachment.

Explanation:

Given linear inequality:

`y < 3x`

When graphing inequalities, temporarily replace the inequality sign for the equals sign:

`\implies y=3x`

Find two points on the line by substituting two values of x into the equation:

`x=0 \implies y=3(0)=0 \implies (0, 0)`

`x=1 \implies y=3(1)=3 \implies (1,3)`

When graphing inequalities:

• < or > : dashed line.
• ≤ or ≥ : solid line.
• < or ≤ : shade under the line.
• > or ≥ : shade above the line.

Therefore, to graph the given linear inequality:

• Plot points (0, 0) and (1, 3).
• Draw a dashed straight line through the points.
• Shade under the dashed line.

Answer 2

Given inequality:

• y < 3x

To graph it first, consider line:

• y = 3x

Find two points on the line.

• x = 0 ⇒ y = 3*0 = 0, so the point is (0, 0)

• x = 1 ⇒ y = 3*1 = 3, the point is (1, 3)

Now, plot the two points.

Next, draw a dashed line trough the two points. Dashed line because the line is not included into solution set, due to '<' sign.

The last step, shade the area below (to the right) the line. Below the line because 'y <' means 'y-values less than' which appears below the line.