Question

Which of the following inequalities matches the graph? (1 point)

Answer 1

Answer:

$6x-y< -3$

The graph in the attached figure

Step-by-step explanation:

Step 1

Find the equation of the line

we have

$A(0, 3), B(1, 9)$

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute

$m=\frac{9-3}{1-0}$

$m=\frac{6}{1}=6$

The equation of the line into slope intercept form is equal to

$y=mx+b$

where

m is the slope

b is the y-intercept

In this problem we have

$m=6$

$b=3$  ------> the y-intercept is the point B

substitute

$y=6x+3$

Step 2

Find the equation of the inequality

we know that

The solution is the shaded area above the dashed line

so

the inequality is equal to  

$y>6x+3$

rewrite

$-6x+y>3$ ------> multiply by $-1$ both sides

$6x-y< -3$

Step 3

Using a graphing tool

The x-intercept is the point $(-0.5,0)$

The y-intercept is the point $(0,3)$

The slope of the dashed line is positive

the graph in the attached figure

Answer 2

the correct answer is 6x − y < −3