Question

The following ordered pairs are solutions to a linear equation: (-20, 11.5), (-21, 12), and (-22, 12.5).

Which of the following graphs shows all of the ordered pairs in the solution set of this linear equation?

Answer 1

The answer is A

Explanation:

You are automatically able to eliminate b and d and based on the data given A makes the most logical sense out of A and D

Answer 2

The generic equation of the line is:

`y-yo = m (x-xo)`
Where,
m: slope of the line
(xo, yo): ordered pair that belongs to the line
The slope is given by:

`m=(y2-y1)/(x2-x1)`
Substituting values we have:

`m=(12-11.5)/(-21-(-20))`
Rewriting we have:

`m=(0.5)/(-21+20)`

`m=(0.5)/(-1)`

`m=-0.5`
By choosing an ordered pair we have:

`(xo, yo) = (-21, 12)` Substituting values in the generic equation:

`y-12=-0.5(x-(-21))`
Rewriting:

`y=-0.5(x+21)+12`

`y=-0.5x-10.5+12`

`y=-0.5x+1.5`
Answer:
the ordered pairs in the solution set of this linear equation is given by:
Option A