To determine the system of equations from the information provided, we'll analyze the given details:
-
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 \( x = 0 \)):
\[ y = 5x + 0 \quad \text{or simply} \quad y = 5x \]
-
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:
- \( y = 5x \) (solid line)
- \( y = 5x + 3 \) (dotted line)
In summary, the system of equations can be represented as: \[ \begin{align*} y &= 5x \ y &= 5x + 3 \end{align*} \]
7 answers