Question

What is the system of equations shown in the graph?

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

x
x
.

The equation of the dotted line is y=
y
=

x
x
+
.
Dotted line has a point, (0, 3)
Solid line has, (0, 0) and (1, 5)

Answer 1

To determine the system of equations from the information provided, we'll analyze the given details:

1. **Solid line**: It has points (0, 0) and (1, 5).
- The two points can help us find the equation of the solid line. The slope \( m \) between these two points is calculated as follows:

\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 0}{1 - 0} = 5
\]

- Using the slope-intercept form of the line \( y = mx + b \), where \( b \) is the y-intercept (which is 0 when \( x = 0 \)):

\[
y = 5x + 0 \quad \text{or simply} \quad y = 5x
\]

2. **Dotted line**: It passes through the point (0, 3). Since we need more information about the slope of the dotted line, we can assume it might have a general form like \( y = mx + b \). Since it intersects the y-axis at (0, 3), we know:

\[
b = 3 \quad \text{(y-intercept)}
\]

- The equation of the dotted line is then \( y = mx + 3 \).

Without additional information, we cannot determine the slope \( m \). However, if we assume that the dotted line is parallel to the solid line (which we often consider in systems of equations), the slope would also be 5. Thus the equation could be:

\[
y = 5x + 3
\]

Therefore, the system of equations based on your description would be:

1. \( y = 5x \) (solid line)
2. \( y = 5x + 3 \) (dotted line)

In summary, the system of equations can be represented as:
\[
\begin{align*}
y &= 5x \\
y &= 5x + 3
\end{align*}
\]