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?

Answer 1

a = 6 is the desired value.

Explanation:

Let two points be A and B , where A = (2,-2) and B = (-6,2)

Now, slope of the line AB
`m= (y_2 - y_1)/(x_2  - x_1)`

or,
`m = (2-(-2))/(-6 -2)   = (4)/(-8)  = (-1)/(2)`

So, the slope m = -(1/2)

Now the general form of the equation is given by

y - y0 = m (x-x0) : where (x0, y0) is any point on the line of the equation.

So, here let (x0,y0) = (2, -2) and m = -1/2

The equation becomes : y -(-2) = (-1/2)(x-2)

or, x + 2y = -2 ia the formed equation.

Now here substiture thepoint (a, -4)

we get: a + 2(-4) = -2

or, a = -2 + 8 = 6

or a = 6 is the desired value.