Solution:
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
- [tex]\rightarrow \text{Slope = m} = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
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.
- [tex]\rightarrow \frac{y_{2} - y_{1} }{x_{2} - x_{1} } = \text{Slope of green line}[/tex]
- [tex]\rightarrow \frac{0 - 4 }{-4 - 0 } = \text{Slope of green line}[/tex]
- [tex]\rightarrow \frac{-4 }{-4} = \text{Slope of green line}[/tex]
- [tex]\rightarrow 1 = \text{Slope of green line}[/tex]
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.
- [tex]\text{y-intercept} = 4[/tex]
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.
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.
- [tex]\rightarrow \frac{y_{2} - y_{1} }{x_{2} - x_{1} } = \text{Slope of green line}[/tex]
- [tex]\rightarrow \frac{0 - 4 }{2 - 0 } = \text{Slope of green line}[/tex]
- [tex]\rightarrow \frac{-4}{2} = \text{Slope of green line}[/tex]
- [tex]\rightarrow -2 = \text{Slope of green line}[/tex]
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.
- [tex]\text{y-intercept} = 4[/tex]
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
