Determine the value of A so that the line whose equation is Ax+y-2=0 is perpendicular to the line containing the point (1,-3) and (-2,4).

Question

Determine the value of A so that the line whose equation is Ax+y-2=0 is perpendicular to the line containing the point (1,-3) and (-2,4).

Answer 1

Shalena,

 

The slope of the line containing points (1,-3) and (-2,4)=Δy/Δx=(-3-4)/(1-(-2))=-7/3

 

The line Ax+y-2=0 can be rewritten y=-Ax+2 in slope-intercept form.  The slope is -A and y-intercept is 2

 

In order for two lines to be perpendicular, the product of their slopes must equal -1

 

So (-7/3)(-A)=-1 and A=-3/7

Answer 2

For this problem we need the equation of the line containing the point (1,-3) and (-2,4).

The slope is the rise over run going from left to right on the x-axis would make (-2,4) or first point on the line.

m = (y₂ - y1)/(x₂ - x₁) = (-3 - 4)/(1 - -2) = -7/3

 

The slope of the perpendicular line and the value of A = -1/m = 3/7

Answer 3

First, we need to get the given line in y=mx+b form, where m is slope and b is y-intercept.
 
y = -Ax + 2
 
 
Now this line is perpendicular to the line that passes though the points.  We need to find the equation of this line. We only need to find the slope, since perpendicular lines have negative reciprocal slopes.
 
m = (y₂ - y₁) / (x₂ - x₁)
m = (4 - (-3)) / (-2 - 1)
m = 7 / -3
m = -7/3
 
The equation of the line that passes though the point is
 
y = (-7/3)x + b
 
 
Therefore,
 
A = -3/7

Answer 4

points (1,-3) and (-2,4)

slope=(4-[-3])/(-2-1)=7/(-3)

y=mx+b

y=(-7/3)x+b

pick one of the points and substitute if you want to find b, but you don't have to

Ax+y-2=0

y=-Ax+2

the line perpendicular to the given line we found has a slope that is the negative reciprocal of (-7/3)

the negative reciprocal of (-7/3) is 3/7

therefore -A=3/7 and A=-3/7

 

Answer 5

First, we need to get the given line in y=mx+b form, where m is slope and b is y-intercept.

 

y = -Ax + 2

 

 

Now this line is perpendicular to the line that passes though the points.  We need to find the equation of this line. We only need to find the slope, since perpendicular lines have negative reciprocal slopes.

 

m = (y₂ - y₁) / (x₂ - x₁)

m = (4 - (-3)) / (-2 - 1)

m = 7 / -3

m = -7/3

 

The equation of the line that passes though the point is

 

y = (-7/3)x + b

 

 

Therefore,

 

A = -3/7