Answer:
The slope-intercept form of the perpendicular line is y = [tex]\frac{1}{3}[/tex] x - 6
Step-by-step explanation:
The product of the slopes of the perpendicular lines is -1
The slope-intercept form of the linear equation is y = m x + b, where
∵ The equation of a line is y = -3x + 6
→ Compare it with the form of the equation above to find m
∴ m = -3
→ Reciprocal it and change its sign to find the slope of the ⊥ line
∵ The reciprocal of -3 with the opposite sign is [tex]\frac{1}{3}[/tex]
∴ m⊥ line = [tex]\frac{1}{3}[/tex]
→ Substitute it in the form of the equation above
∴ y = [tex]\frac{1}{3}[/tex] x + b
→ To find b substitute x and y in the equation by the coordinates
of a point on the line
∵ The perpendicular line goes through (12, -2)
∴ x = 12 and y = -2
∵ -2 = [tex]\frac{1}{3}[/tex] (12) + b
∴ -2 = 4 + b
→ Subtract 4 from both sides
∴ -2 - 4 = 4 - 4 + b
∴ -6 = b
→ Subustitute it in the equation above
∴ y = [tex]\frac{1}{3}[/tex] x + -6
∴ y = [tex]\frac{1}{3}[/tex] x - 6
The slope-intercept form of the perpendicular line is y = [tex]\frac{1}{3}[/tex] x - 6
