Question

Graph the linear inequality y < 1/2x + 2 using slope-intercept form.

Answer 1

See attachment.

Explanation:

Given linear inequality:

`y < (1)/(2)x+2`

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

`\implies y=(1)/(2)x+2`

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

`x=0 \implies y=(1)/(2)(0)+2 =2\implies (0, 2)`

`x=4 \implies (1)/(2)(4)+2=4 \implies (4,4)`

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, 2) and (4, 4).
• Draw a dashed straight line through the points.
• Shade under the dashed line.

Answer 2

Given inequality:

• y < 1/2x + 2

To graph it first, consider line:

• y = 1/2x + 2

Find two points on the line.

Let them be x- and y-intercepts:

• x = 0 ⇒ y = 1/2*0 + 2 = 2, so the point is (0, 2)
• y = 0 ⇒ 0 = 1/2x + 2 ⇒ 1/2x = - 2 ⇒ x = - 4, the point is (- 4, 0)

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 the line. Below the line because 'y <' means 'y-values less than' which appears below the line.