Question

The graph of a linear equation contains the points (4,1) and (-2,-11). Which point also lies on the graph?

A. (1,1)
B.(1,-5)
C.(1,-2)
D.(1,-7)

Answer 1

Option B is correct.

(1 , -5) lies on the graph.

Explanation:

Given the points (4,1) and (-2 , -11)

First find the linear equation for the given points.

Equation of line for two points
`(x_1, y_1)` and
`(x_2, y_2)`

is given by:
`y-y_1 = ((y_2-y_1)/(x_2 - x_1)) (x-x_1)`

Substitute the given points (4,1) and (-2 , -11) in above equation to find the equation of line:

`y-1=((-11-1)/(-2-4))(x-4)`

or

`y-1=((-12)/(-6))(x-4)`

or

`y-1=2(x-4)`

Using distributive property on RHS ( i.e,
`a\cdot (b+c) = a\cdot b+ a\cdot c` )

we have;

y -1 = 2x-8

Add 1 to both sides of an equation;

y-1+1 = 2x-8+1

Simplify:

y = 2x -7

Therefore, the equation of line for the given point is: y =2x - 7 ....[1]

To find which points lies on the graph ( i.e, Line)

Substituting the given options in equation [1] we have;

A . (1,1)

Put x =1 and y =1

`1 = 2\cdot 1 -7 = 2-7`

1 = -5 which is not true.

Similarly

B. for (1, -5)

`-5= 2\cdot 1 -7 = 2-7`

-5 = -5 which is true.

C. for (1, 2)

`2= 2\cdot 1 -7 = 2-7`

2 = -5 which is not true.

And

D. For (1 , -7)

`-7= 2\cdot 1 -7 = 2-7`

-7 = -5 which is also not true.

Therefore, the only point which lies on the line graph [1] is; (1 ,-5)