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

option A

Explanation:

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

Frame the equation of line y=mx+b using ordered pairs

(-20, 11.5), (-21, 12)

`slope m = (y_2-y_1)/(x_2-x_1) =(12-11.5)/(-21+20)=-0.5`

m= -0.5

Now plug in (-21,12) and find out b

y=mx+b

12= -0.5(-21) + b

12= 10.5 +b

Subtract 10.5 on both sides

So b= 1.5

Equation of line is y=-0.5x + 1.5

Slope is negative so graph will be decreasing

Option A and option C graphs are decreasing

y intercept is the b values = 1.5

y intercept is (0,1.5)

Lets find x intercept

Plug in 0 for y in the equation y=-0.5x+1.5

0 = -0.5x+1.5

subtract 1.5 on both sides

1.5 = -0.5x

Divide by -0.5

so x= 3

So x intercept is (3,0)

Option A graph has x intercept (3,0) and y intercept (0,1.5)