Question

A is the point (2, 3) and B is the point (7,-5).Find the equation of the line
through A that is perpendicular to AB. Give your answer in the form y =
mx+C.

Answer 1

Step-by-step explanation:

Find the gradient of AB

-2.5

Find the gradient of perpendicular

0.4

Make the equation

y= 0.4x + c

Apply point A

3= 0.4*2+c

3-0.8= c

c= 2.2

y= 0.8x + 2.2

Answer 2

Answer:

y=0.625x+1.75

Step-by-step explanation:

The equation of the line that goes through (2, 3) and (7, -5) needs to be found before finding the equation perpendicular to it. The formula y=mx+c will be used for finding this equation.

Calculating the slope between the data points:

$m1=\frac{3-(-5)}{2-7}=\frac{8}{-5}=-1.6$

Finding the first y-intercept:

$y=mx+c$

$c=y-mx$

$c=3-(-1.6*2)=3+3.2=6.2$

The equation for the line that goes through the points is:

$y=-1.6x+6.2$

The perpendicular slope will be the opposite reciprocal of the original slope.

The second slope is found by first multiplying the first slope (m1) by -1:

$m2=m1*-1=-1.6*-1=1.6$

Then by taking the reciprocal:

$m2=\frac{1}{1.6} =0.625$

The second equation must have an intercept that goes through point A:

$c=y-mx$

$c=3-(0.625*2)=3-1.25=1.75$

The perpendicular equation is:

$y=0.625x+1.75$