Line AB and Line BC form a right angle at point B.

Question

If A = (-3, -1) and B = (4, 4), what is the equation of Line BC?

A. 

x + 3y = 16

B. 

2x + y = 12

C. 

-7x − 5y = -48

D. 

7x − 5y = 48

Answer 1

You are given two points which define a line: (-3, -1) and (4, 4).

First find the slope. It may be that only one of the multiple-choice lines has that slope and you won't have to do any more calculations.

The slope is the difference of the y-coordinates over the difference in the corresponding x-coordinates. Difference is found by subtracting.

–1 – 4

_______ = SLOPE

–3 – 4

–5 5

____ = ____

–7 7

Now, let's quickly rewrite the multiple-choice equations into slope-intercept form so that we can see if any of the lines have a slope of 5/7.

A. 

x + 3y = 16

3y = –x + 16

Will stop here, since the slope will be negative. We are looking for a POSITIVE slope.

B. 

2x + y = 12

y = –2x + 12

The slope is –2 (the coefficient of the x term when the line is written in slope-intercept form). This is not our line.

C. 

-7x − 5y = -48

–5y = 7x – 48 (Now I will divide each side by –5.)

y = (7/–5)x + (48/5)

The opposite of the slope that we want.

D. 

7x − 5y = 48

–5y = –7x + 48 (Now I will divide each side by –5.)

y = (7/5)x + (48/–5)

Hey, hey! This is the only line that has the slope of 7/5. Therefore, we didn't need to do anything more, in this case, than figure out the slope of the line in question.

Answer 2

Draw the two points and Draw a possible triangle with point C.

The slope of the line AB and that of the line BC are perpendicular

Find the slope of the line AB: m=(4-(-1)))/(4--3) = 5/7 (from point A run 7 units and rise 5 units to get to B)

The slope of any line perpendicular: m_perp= -7/5 (run 5 units in the opposite direction, and rise 7 units)

Now you have the slope and the point B(4,4) on the line:

Set up the point-slope form to get the equation: y-4=-7/5 *(x-4)

Simplify to get the slope-intercept form y=mx+b:

y= - 7/5 *x +28/5 +4= - 7/5 *x +48/5

Final answer:

y= -7/5 x +9.6 (if you graph the line, the y-intercept is at 9.6)