Identify the system of equations given in the graph below.

Hi there!

From the graph, we can see that both lines are parallel. We can determine the slope of one line to find the slope of the other.

Use the slope formula to determine the slope of a line. In this case, I am using the blue line as a reference:

The slope of both lines is 3.

Let's find the equation of the blue line by finding its y-intercept to solve for the "b" value in the equation y= mx + b:

y-intercept is when x = 0, or at (0, 1). Therefore:

Blue line equation: y = 3x + 1

The red line intersects the y-axis at (0, -1), therefore:

Red line equation: y = 3x - 1

The systems of equations is:

y = 3x + 1

y = 3x - 1

answer: 5

step-by-step explanation:

since, the range is the difference between the lowest and highest values of the given sample space.

and, here the sample space = { 3, 1, 0, 4, 1, 4, 2, 3, 0, 5, 0, 1, 1, 2, 0, 4, 1,4, 4 ,2 ,3 ,2 ,0 ,1 ,4 }

here, the highest value of the given sample = 5

and, the lowest value = 0

therefore, the range of the sample space = 5 - 0 = 5

18 units²

step-by-step explanation:

first let's find altitude bd using the distance formula

d = √((y₂ - y₁)² + (x₂ - x₁)²)

bd = √((0 - -3)² + (0 - 3)²)

bd = √18

given the placement of points a and c, we can denote that point d bisects segment ac.

we will call ac the base.

using the distance formula

ac = √((0 - 6)² + (-6 - 0)²)

ac = √72

knowing our base and our height, we can plug these into our triangle area formula

area = (b * h)/2

area = (√18 * √72) / 2

area = (√1296) / 2

area = 36 / 2

area = 18 units²