Question

How Do You Graph This Equation

Answer 1

See below ~

Explanation:

Inequality 1 :

• Convert into y = mx + b form
• 2y ≤ x - 10
• y ≤ x/2 - 5

Taking 2 points :

• 0 ≤ x/2 - 5
• x/2 ≥ 5
• x ≥ 10
• ⇒ Point 1 = (10, 0)

• y ≤ 0 - 5
• y ≤ -5
• ⇒ Point 2 = (0, -5)

Inequality 2 :

• x + y ≤ -3
• y ≤ -x - 3

Taking 2 points :

• 0 ≤ -x - 3
• x ≤ -3
• Point 1 = (-3, 0)

• y ≤ 0 - 3
• y ≤ - 3
• Point 2 = (0, -3)

Plot the two 2 lines using the 2 points and shade as per the sign of the inequality. The result will be this graph :

Answer 2

Rearrange both inequalities to make y the subject.

Momentarily swap the inequality sign for an equals sign in order to calculate two points for each line.

Inequality 1

`2y \leq x-10`

`\implies y < (1)/(2)x-5`

`x=0\implies y=(1)/(2)(0)-5 \implies (0,-5)`

`x=4 \implies y=(1)/(2)(4)-5 \implies (4,-3)`

Inequality 2

`x+y\leq -3`

`\implies y\leq -x-3`

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

`x=4\implies y=-(4)-3\implies (4,-7)`

When graphing inequalities

< or > : dashed line

≤ or ≥ : solid line

< or ≤ : shade below the line

> or ≥ : shade above the line

Therefore,

Inequality 1: plot points (0, -5) and (4, -3) and draw a solid line through them.

Inequality 2: plot points (0, -3) and (4, -7) and draw a solid line through them.

Shade the area below both lines from where the lines intersect.