Question

A line passes through the points (2, –2) and (–6, 2). The point (a, –4) is also on the line. What is the value of a? mc023-1.jpg

Answer 1

Answer:

$a=6$

Step-by-step explanation:

We have been given coordinates of three points on the same line and we are asked to find the value of 'a'.      

First of all, we will find the equation of the line in slope-intercept form of equation $y=mx+b$.

Let us find slope of our given line using coordinates of point $(2,-2)$ and $(-6,2)$.

Upon substituting the coordinates of the given points in slope formula we will get,

$m=\frac{2--2}{-6-2}$

$m=\frac{2+2}{-8}$

$m=\frac{4}{-8}$

$m=-\frac{1}{2}$

Now, we will substitute $m=-\frac{1}{2}$ and coordinates of point $(2,-2)$ in slope-intercept form of equation to find the y-intercept.

$-2=-\frac{1}{2}*2+b$

$-2=-1+b$

$-2+1=-1+1+b$  

$-1=b$

Therefore, the equation of line passing through the given points is $y=-\frac{1}{2}x-1$.

To find the value of 'a' we will substitute coordinates of point $(a,-4)$ in our equation as:

$-4=-\frac{1}{2}*a-1$

$-4+1=-\frac{1}{2}*a-1+1$

$-3=-\frac{1}{2}*a$

Upon multiplying both sides of our equation by -2, we will get

$-3*-2=-\frac{1}{2}*a*-2$

$6=a$

Therefore, the value of a is 6.

Answer 2

Find the equation of the line thru (2, -2) and (-6, 2):
                        2-(-2)         4
slope is m  = ----------- =  ----- = -1/2
                        -6-2           -8

Then the equation of this line is (in point-slope form) y-2 = (-1/2)(x-[-6]), or
              x+6
y-2 = - ---------
                2

Now (a, -4) must also be on this line.  So, let y=-4 and find a:
                a+6                          a+6
-4-2   =  - ---------- , or   -6 = - --------- 
                  2                                2

Then -12 = -(a+6), or a+6 = 12   =>        a=2 (answer)