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)

Option B is correct.

(1 , -5) lies on the graph.

Step-by-step explanation:

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

First find the linear equation for the given points.

Equation of line for two points and  

is given by:  

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

or

or

Using distributive property on RHS ( i.e,   )

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 = -5 which is not true.

Similarly

B. for (1, -5)

-5 = -5 which is true.

C. for (1, 2)

2 = -5 which is not true.

And

D.  For (1 , -7)

-7 = -5 which is also not true.

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