Question

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

Answer 1

You get the equation to be y=2x-7. You can just plug them in and you find out the answer is B.

Answer 2

Answer:

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 $(x_1, y_1)$ and  $(x_2, y_2)$

is given by:   $y-y_1 = (\frac{y_2-y_1}{x_2 - x_1}) (x-x_1)$

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

$y-1=(\frac{-11-1}{-2-4})(x-4)$

or

$y-1=(\frac{-12}{-6})(x-4)$

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)