Question

Plot six lines. Each line should pass through the origin and one of the six points. One is done for you.

Answer 1

Solution (Line 2): (Refer to graph 1)

Note that:

• Given points: (0, -2) and (1, -4)
• Slope formula: Rise/Run
• Point slope form formula: y - y₁ = m(x - x₁)

To create the equation of the line, find the slope. Then, use point slope form to find the equation of the line.

Use the slope formula to find the slope.

• Rise/Run = Slope
• => Rise = -2; Run = 1
• => Rise/Run = -2/1 = -2

Use the point slope form formula.

• y - y₁ = m(x - x₁) = Equation of line.
• => y - (-4) = -2(x - 1) = Equation of line.
• => y + 4 = -2x + 2
• => y = -2x + 2 - 4
• => y = -2x - 2

Solution (Line 3): (Refer to graph 2)

Note that:

• Given points: (0, -2) and (-4, 3)
• Slope formula: Rise/Run
• Point slope form formula: y - y₁ = m(x - x₁)

To create the equation of the line, find the slope. Then, use point slope form to find the equation of the line.

Use the slope formula to find the slope.

• Rise/Run = Slope
• => Rise = -5; Run = 4
• => Rise/Run = -5/4

Use the point slope form formula.

• y - y₁ = m(x - x₁) = Equation of line.
• => y - 3 = -5/4{x - (-4)} = Equation of line.
• => y - 3 = -5/4{x + 4}
• => y - 3 = -5x/4 - 5
• => y = -5x/4 - 2

Solution (Line 4): (Refer to graph 3)

Note that:

• Given points: (0, -2) and (-3, -5)
• Slope formula: Rise/Run
• Point slope form formula: y - y₁ = m(x - x₁)

To create the equation of the line, find the slope. Then, use point slope form to find the equation of the line.

Use the slope formula to find the slope.

• Rise/Run = Slope
• => Rise = 3; Run = 3
• => Rise/Run = 3/3 = 1

Use the point slope form formula.

• y - y₁ = m(x - x₁) = Equation of line.
• => y - (-5) = 1{x - (-3)} = Equation of line.
• => y - (-5) = 1{x + 3}
• => y + 5 = x + 3
• => y = x - 2

Hoped this helped!