Question

Graph the line perpendicular to y=−3/2x+1 that passes through the point at (−3, −4).

Answer 1

Step-by-step explanation:

perpendicular line has slope m = -1/m

m of perpendicular line = -3/2

slope of required line = 2/3

equation = y-y1 = m(x-x1)

y-(-4) = 2/3(x-(-3))

y+4 = 2(x+3)/3

3y+12 = 2x+6

2x-3y-6 =0

Answer 2

Concept:

The product of slopes of two perpendicular lines is equal to -1.

Given:

A line y = −3/2x +1 and a point at (−3, −4).

Find:

A line perpendicular to y = −3/2x +1 passes through (−3, −4).

Solution:

Slope of the line, y = −3/2x +1 is m₁  = -3/2

As we know, the product of slopes of two perpendicular lines is equal to -1,

m₁ m₂ = -1

So, the perpendicular line has a slope

m₂ = -1/m₁

m₂ = -1/(-3/2)

m₂ = 2/3

Hence, the equation of the line can be written as y = 2/3x + c.

Line y = 2/3x + c, passes through (−3, −4).

(-4) = 2/3 × (-3) + c

c = - 4 + 2

c = -2

So, the equation of the line is y = 2/3 x - 2.

The graph of the line y = 2/3 x - 2 is attached.

Hence, the equation the line perpendicular to y=−3/2x+1 that passes through the point at (−3, −4) is y = 2/3 x - 2.

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