Answer:
y = -½x + 12; y = 2x + 2
Step-by-step explanation:
1. Solve the equation
y = -½x + 6
(a) Let x = 0
y = -½(0) + 6
y = 0 + 6
y = 6
(b) Let y = 0
0 = -½x + 6 Subtract 6 from each side
-6 = -½x Multiply each side by -2
x = 12
The line passes through the points (0, 6) and (12, 0).
2. Equation for parallel line
The line passes through (4, 10).
y = mx + b
m = -½
10 = -½(4) + b
10 = -2 + b Add 1 to each side
b = 12
The equation for the parallel line is y = -½x + 12.
3. Equation for perpendicular line
(a). Find the slope (m₁) of the original line
The equation for the original line is
y = -½x + 6
slope = m₁ = -½
(b). Find the slope (m₂) of the perpendicular line
m₂ = -1/m₁ Substitute the value of m₁
m₂ = 2
(c). Find the equation for the perpendicular line
y = mx + b Substitute the value of m₂
y = 2x + b
The line passes through (4,10).
10 = 2 × 4 + b
10 = 8 + b Subtract 8 from each side
b = 2
y = 2x + 2
In the image, below, the red line is the graph of your original equation.
The green line passing through (4, 10) is the parallel line.
The black line passing through (4, 10) is the perpendicular line.
