Answer:
y = 2x + 8
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Given
x + 2y - 12 = 0 ( subtract x - 12 from both sides )
2y = - x + 12 ( divide terms by 2 )
y = - [tex]\frac{1}{2}[/tex] x + 6 ← in slope- intercept form
with slope m = - [tex]\frac{1}{2}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{1}{2} }[/tex] = 2
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To find the x- intercept let y = 0 in the equation and solve for x
3x - 2(0) + 12 = 0
3x + 12 = 0 ( subtract 12 from both sides )
3x = - 12 ( divide both sides by 3 )
x = - 4
Then x- intercept at (- 4, 0 )
Then
y = 2x + c ← is the partial equation
To find c substitute (- 4, 0) into the partial equation
0 = - 8 + c ⇒ c = 0 + 8 = 8
y = 2x + 8 ← equation of perpendicular line
