Question

Write and equation for each line

Answer 1

To find the equation of all the lines, we must:

1. Find the slope

• Choose any two points
• Substitute the coordinates into the slope formula
• Solve for the slope.

2. Find the y-intercept by looking at the graph

Finding the equation of the green line:

Step-1: Choose any two points on the line

• Chosen points: (0, 4) and (-4, 0)

Step-2: Review the slope formula

• 
  `\rightarrow \text{Slope = m} = (y_(2) - y_(1) )/(x_(2) - x_(1) )`

Where:

• x₁ = x coordinate of the first point
• x₂ = x coordinate of the second point
• y₁ = y coordinate of the first point
• y₂ = y coordinate of the second point

Step-3: Substitute the coordinates into the slope formula.

• 
  `\rightarrow (y_(2) - y_(1) )/(x_(2) - x_(1) ) = \text{Slope of green line}`
• 
  `\rightarrow (0 - 4 )/(-4 - 0 ) = \text{Slope of green line}`
• 
  `\rightarrow (-4 )/(-4) = \text{Slope of green line}`
• 
  `\rightarrow 1 = \text{Slope of green line}`

Step-4: Find the y-intercept of the green line

The y-intercept is the intersection of the line on the y-axis. Looking at the graph, we can tell that the intersection of the y-axis made by the green line is 4.

• 
  `\text{y-intercept} = 4`

Step-5: Create the equation

• Slope intercept form: y = (m)x + (b) [m = slope; b = y-intercept]
• Equation of green line: y = (1)x + (4) [m = 1; b = 4]
• Equation of green line: y = x + 4

Finding the equation of the yellow line

The yellow line is a vertical line intersecting (1,0). Since the y-coordinate is 0, the equation will be:

• x = x coordinate of (1,0)

The x coordinate of (1,0) is 1.

• x = 1

Finding the equation of the blue line

Step-1: Choose any two points on the line

• Chosen points: (0, 4) and (2, 0)

Step-2: Substitute the coordinates into the slope formula.

• 
  `\rightarrow (y_(2) - y_(1) )/(x_(2) - x_(1) ) = \text{Slope of green line}`
• 
  `\rightarrow (0 - 4 )/(2 - 0 ) = \text{Slope of green line}`
• 
  `\rightarrow (-4)/(2) = \text{Slope of green line}`
• 
  `\rightarrow -2 = \text{Slope of green line}`

Step-3: Find the y-intercept of the green line

Looking at the graph, we can tell that the intersection of the y-axis made by the blue line is 4.

• 
  `\text{y-intercept} = 4`

Step-4: Create the equation

• Slope intercept form: y = (m)x + (b) [m = slope; b = y-intercept]
• Equation of green line: y = (-2)x + (4) [m = -2; b = 4]
• Equation of green line: y = -2x + 4