Use the image to answer the question.

Question

Two lines intersect on the coordinate plane. Both axes range from negative 10 to 10 in increments of 1.

What is the system of equations shown in the graph?

(2 points)
The equation of the solid line is y=

x
.

The equation of the dotted line is y=

x
+
.

Answer 1

To determine the system of equations based on the description of the graph, let's define the lines:

1. Solid Line Equation: Since the solid line is represented by \( y = x \), it indicates that for every unit increase in \( x \), \( y \) increases by the same amount.

2. Dotted Line Equation: Let's assume a generic form for the dotted line, which has the equation \( y = x + b \), where \( b \) is the y-intercept.

To find the exact value of \( b \):

• Observation of the Graph: If you can see the graph, identify the point where the dotted line crosses the y-axis. For instance, if it crosses at (0, 2) that means \( b = 2 \).

For example, if the dotted line intersects at (0, 2), then the equation of the dotted line would be:

\[ y = x + 2 \]

So the system of equations based on your description would be:

• Solid Line: \( y = x \)
• Dotted Line: \( y = x + 2 \)

You could fill in the blanks as follows:

• The equation of the solid line is \( y = x \).
• The equation of the dotted line is \( y = x + 2 \).

Make sure to adjust the value of \( b \) based on what you see in the graph!

Answer 2

the dotted line has two dots, 0,3, and 1,5, with 1,5 also being on the solid line, too, this is the point where the lines intersect. the other one on the solid line is 0,0. can this help you solve the equation?