Finding x and b in the following

Question

Find x so that the given points are collinear. (9, -12) (13, 4) (x, 14)

 

A line with slope of -4 contains the points (2, -8) and (7, b). What is b?

 

Answer 1

Hi Madison,

 

Regarding your first 3 points

(9,-12) (13,4)(x,14)

 

In order for all three points to be collinear they must be on the same line.

 

Using the first 2 points we can determine the equation of the line

y-y₁ = m (x-x₁)

where m is the slope and (x₁,y₁) is one of the given points.

 

The slope is

m = (y2-y1)/(x2-x1) = ([4-(-12)]/(13-9) = 16/4 = 4

y-4 = 4(x-13)

Let's solve this for y

y-4 = 4x-52

y = 4x-48

 

Now we need to find the x in the point (x,14)

We can evaluate the equation of the line we determined above for the point and solve for x.

y = 4x-48

14 = 4x-48

62 = 4x

15.5 = x

 

 

Now for the second set of points.

 

Using the point slope form of an equation of a line.

y-(-8) = (-4)(x-2)

y+8 = -4x+8

y = 4x

 

Evaluation this equation using the point (7,b)

y = 4x

b = (4)(7)

b = 28

 

Answer 2

I think b should be -28.