Which of the following inequalities matches the graph? A. −6x + y < 3
B. 6x + y < 3
C. 6x − y < −3
D. The correct inequality is not listed

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

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

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

x2−x1

y2−y1

substitute

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

1−0

9−3

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

1

6

=6

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

y=mx+by=mx+b

where

m is the slope

b is the y-intercept

In this problem we have

m=6m=6

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

substitute

y=6x+3y=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+3y>6x+3

rewrite

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

6x-y < -36x−y<−3

Step 3

Using a graphing tool

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

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

The slope of the dashed line is positive

the graph in the attached figure

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions