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25 votes
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Write the equation of the line that is perpendicular to y = -2/3 x +2 and goes through the point (-1, 4). Make sure your final answer is in slope-intercept form

User NMrt
by
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1 Answer

7 votes
7 votes

Given:

The equation of a line is


y=-(2)/(3)x+2 ...(i)

The perpendicular line passes through the point (-1,4).

To find:

The equation of the perpendicular line.

Solution:

The slope intercept form of a line is:


y=mx+b ...(ii)

Where, m is the slope and b is the y-intercept.

On comparing (i) and (ii), we get


m=-(2)/(3)

Product of slopes of two perpendicular lines is -1.

Let the slope of perpendicular line is
m_1.


m* m_1=-1


-(2)/(3)* m_1=-1


m_1=(3)/(2)

The slope of the perpendicular line is
m_1=(3)/(2) and it passes through the point (-1,4). So, the equation of the line is:


y-y_1=m_1(x-x_1)


y-4=(3)/(2)(x-(-1))


y-4=(3)/(2)(x+1)


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

Add 4 on both sides.


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


y=(3)/(2)x+(3+8)/(2)


y=(3)/(2)x+(11)/(2)

Therefore, the equation of required line is
y=(3)/(2)x+(11)/(2).

User Mfalade
by
2.7k points
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