Question

1. use the graph to answer a and b.

a. which two equations are graphed above?
1:
2:
b. what ordered pair satisfies both equations?

Explanation:

Part a: Finding the equations of the two lines

Step 1: Analyze Line 1

Line 1 passes through the points \((18, 0)\) and \((12, 12)\) (the intersection point). Let's find the slope \(m_1\) first. The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For Line 1, using \((x_1,y_1)=(18,0)\) and \((x_2,y_2)=(12,12)\), we have:

$$m_1=\frac{12 - 0}{12 - 18}=\frac{12}{-6}=-2$$

Now, use the point - slope form \(y - y_1=m(x - x_1)\). Using the point \((18,0)\) and \(m_1=-2\):

$$y-0=-2(x - 18)$$

$$y=-2x + 36$$

Step 2: Analyze Line 2

Line 2 passes through the points \((4, 0)\) and \((12, 12)\). Let's find the slope \(m_2\). Using \((x_1,y_1)=(4,0)\) and \((x_2,y_2)=(12,12)\) in the slope formula:

$$m_2=\frac{12 - 0}{12 - 4}=\frac{12}{8}=\frac{3}{2}$$

Using the point - slope form with the point \((4,0)\) and \(m_2 = \frac{3}{2}\):

$$y-0=\frac{3}{2}(x - 4)$$

$$y=\frac{3}{2}x-6$$

So the two equations are \(y=-2x + 36\) (Line 1) and \(y=\frac{3}{2}x - 6\) (Line 2).

Part b: Finding the ordered pair that satisfies both equations

The ordered pair that satisfies both equations is the intersection point of the two lines. From the graph, we can see that the two lines intersect at the point where \(x = 12\) and \(y = 12\). We can also verify this by substituting \(x = 12\) into both equations:

• For \(y=-2x + 36\), when \(x = 12\), \(y=-2(12)+36=-24 + 36 = 12\).
• For \(y=\frac{3}{2}x-6\), when \(x = 12\), \(y=\frac{3}{2}(12)-6=18 - 6 = 12\).

Final Answers

a.

1. \(y=-2x + 36\)
2. \(y=\frac{3}{2}x-6\)

b.

The ordered pair is \((12,12)\)

Answer:

Part a: Finding the equations of the two lines

Step 1: Analyze Line 1

Line 1 passes through the points \((18, 0)\) and \((12, 12)\) (the intersection point). Let's find the slope \(m_1\) first. The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For Line 1, using \((x_1,y_1)=(18,0)\) and \((x_2,y_2)=(12,12)\), we have:

$$m_1=\frac{12 - 0}{12 - 18}=\frac{12}{-6}=-2$$

Now, use the point - slope form \(y - y_1=m(x - x_1)\). Using the point \((18,0)\) and \(m_1=-2\):

$$y-0=-2(x - 18)$$

$$y=-2x + 36$$

Step 2: Analyze Line 2

Line 2 passes through the points \((4, 0)\) and \((12, 12)\). Let's find the slope \(m_2\). Using \((x_1,y_1)=(4,0)\) and \((x_2,y_2)=(12,12)\) in the slope formula:

$$m_2=\frac{12 - 0}{12 - 4}=\frac{12}{8}=\frac{3}{2}$$

Using the point - slope form with the point \((4,0)\) and \(m_2 = \frac{3}{2}\):

$$y-0=\frac{3}{2}(x - 4)$$

$$y=\frac{3}{2}x-6$$

So the two equations are \(y=-2x + 36\) (Line 1) and \(y=\frac{3}{2}x - 6\) (Line 2).

Part b: Finding the ordered pair that satisfies both equations

The ordered pair that satisfies both equations is the intersection point of the two lines. From the graph, we can see that the two lines intersect at the point where \(x = 12\) and \(y = 12\). We can also verify this by substituting \(x = 12\) into both equations:

• For \(y=-2x + 36\), when \(x = 12\), \(y=-2(12)+36=-24 + 36 = 12\).
• For \(y=\frac{3}{2}x-6\), when \(x = 12\), \(y=\frac{3}{2}(12)-6=18 - 6 = 12\).

Final Answers

a.

1. \(y=-2x + 36\)
2. \(y=\frac{3}{2}x-6\)

b.

The ordered pair is \((12,12)\)