what is the equation of a line in slope-intercept form that is perpendicular to the line y=-3x+2 and passes through (3,-1)?
- llafferLv 72 months agoFavorite Answer
Perpendicular lines have negative-reciprocal slopes. The slope of the first line is -3 so the slope of its perpendicular is 1/3.
We have the slope, an x, and a y so we can solve for the unknown intercept:
y = mx + b
-1 = (1/3)(3) + b
-1 = 1 + b
-2 = b
Your equation is:
y = (1/3)x - 2
- 2 months ago
Start with point-slope form. The slope of a perpendicular line is the negative reciprocal of the slope of the original line.
- Engr. RonaldLv 72 months ago
y = - 3x + 2
solving the slope that is perpendicular to y = - 3x + 2
m = - 3
m2 = - 1/(-3) = 1/3
solving for y - intercept using slope intercept form formula.
y = mx + b
- 1 = 1/3(3) + b
- 1= 1 + b
b = - 1 - 1
b = - 2
The equation of the line that is perpendicular to y = - 3x + 2 is
y = 1/3x - 2 Answer//
Any line perpendicular to y = -3x+2 must have slope m = ¹⁄₃
The equation of a line with slope m = ¹⁄₃ and passing through (3,-1) is
y - (-1) = ¹⁄₃ (x - 3)
y = ¹⁄₃ x - 2 .......................ANS
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- la consoleLv 72 months ago
The typical equation of a line is: y = mx + y₀ → where m: slope and where y₀: y-intercept
y = - 3x + 2 ← this is the line (ℓ₁) → the slope is (- 3)
Two lines are perpendicular if the product of their slope is (- 1).
As the slope of the line (ℓ₁) is (- 3), the slope of the perpendicular line (ℓ₂) is (1/3).
The equation of the perpendicular line (ℓ₂) becomes: y = (1/3).x + y₀
The line (ℓ₂) passes through (3 ; - 1), so the coordinates of this point must verify the equation of the line (ℓ₂).
y = (1/3).x + y₀
y₀ = y - (1/3).x → you substitute x and y by the coordinates of the point (3 ; - 1)
y₀ = - 1 - [(1/3) * 3]
y₀ = - 1 - 1
y₀ = - 2
The equation of the line (ℓ₂) is: y = (1/3).x + 2
y = x/3 + c
-1 = 3/3 + c
y = x/3 - 2
- lenpol7Lv 72 months ago
The perpendicular gradient is the negative reciprocal of '-3' , which is '1/3'
Displacing the point against (x,y)
y - - 1 = (1/3)(x - 3)
y + 1 = x/3 - 3/3
y + 1 = x/3 - 1
y = x/3 + 2 or y = (1/3)x + 2