The equation of the line perpendicular to the graph of 4x-2y=9 that passes through the point at ( 2, 6 ) is y=4x+2.
Answer:
y = -½x + 7
Step-by-step explanation:
A. Find the intercepts of the first graph
4x - 2y = 9
(i) Let x = 0
-2y = 9 Divide each side by -2
y = -9/2
(ii) Let y = 0
4x = 9 Divide each side by 4
x = 9/4
The line passes through the points (0, -9/2) and (9/4, 0).
B. Equation for perpendicular line
(i) Find the slope (m₁) of the original line
The equation for the original line is
4x - 2y = 9 Subtract 4x from each side
-2y = -4x + 9 Divide each side by 2
y = 2x - 9/2
slope = m₁ = 2
(ii) Find the slope (m₂) of the perpendicular line
m₂ = -1/m₁ Substitute the value of m₁
m₂ = -½
C. Find the equation for the perpendicular line
y = mx + b Substitute the value of m₂
y = -½x + b
The line passes through (2, 6).
6 = -½ × 2 + b
6 = -1 + b Add 1 to each side
b = 7
y = -½x + 7
In the image, below, the red line is the graph of your original equation.
The blue line passing through (2, 6) is the perpendicular line.
