Question is in description.

Question

Find the equation for the line that passes through the point (−1, 2), and that is perpendicular to the line with the equation 4/3x + 2y = 4/3

Answer 1

Hi Shatoria, the first step is to find the slope of the given line. 

 

Given line:

 

4/3 * x + 2y = 4/3

 

Multiply all terms by 3 to remove the fractions:

 

4x + 6y = 4

 

The slope of a line in the standard form is: -(A/B). Here we have: -(4/6), or -2/3.

 

The slope of a line that is perpendicular to the given line will equal -1 divided by the given line's slope or: -1/m.

 

That gives the slope of the line that is perpendicular as: -1/(-2/3), or 3/2.

 

Knowing the slope of the parallel line and one point, use the point-slope form of the line to find the line.

 

Point-slope form:

 

y - y₁ = m * (x - x₁)

 

y₁ = 2

 

x₁ = -1

 

m = 3 / 2

 

y - 2 = 3 / 2 * (x - (-1))

 

y - 2 = 3 / 2 * x + 3 / 2

 

Add 2 to both sides:

 

y = 3 / 2 * x + 2 + 3 / 2, or

 

y = 3 / 2 * x + 7 / 2

 

Questions?