Write an equation in slope-intercept form for the line that passes through the point ( -2 , -1 ) and is perpendicular to the line − 3 x − 2 y = 4 .

Answer 1

To write an slope-intercept equation (y = mx + b), we will need to find m and b

Given: point (-2, -1) and the equation is perpendicular to the line to be -3x - 2y =4

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First, find the slope of the perpendicular equation

-3x - 2y =4 -> move everything to the right -> y = -3/2x - 2 -> slope = -3/2

1. Because it is perpendicular, the slope of the original equation will be negative reciprocal of the perpendicular line. (search up "relationship between perpendicular lines" if you don't understand)

Therefore, slope of the original equation is 2/3

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Now we have y = 2/3 x + b; plug (-2, -1) into x and y to find b

1. -1 = 2/3 ( -2 ) + b
2. -1 = -4/3 + b
3. b = 1/3

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Plug b into the equation

answer: y = 2/3 x + 1/3

Answer 2

The product of slopes of perpendicular lines is -1. The slope of the given line is

m₁ = -a/b = -(-3)/(-2) = -3/2

The slope of the perpendicular line is

m₂ = -1/m₁ = -1/(-3/2) = 2/3

The equation of the perpendicular line is

y = (2/3)x + b

Find b from the given point.

-1 = (2/3)(-2) + b

You finish from here.