Use the image to answer the question.

Question

double check
Two parallel lines slope upward on a coordinate plane. A dotted line passes through the plotted point left parenthesis 0 comma 0 right parenthesis. A solid line intersects the y-axis at left parenthesis 0 comma 3 right parenthesis.

Write the equations for the system of linear equations graphed.

(1 point)
The equation of the solid line is y=
, and the equation of the dotted line is y=
.

Answer 1

To derive the equations of the lines based on the description given:

1. The solid line intersects the y-axis at \((0, 3)\). This indicates that the y-intercept is 3. Assuming the slope (m) is denoted as \(m_1\), the equation can be expressed as: \[ y = m_1x + 3 \]

2. The two parallel lines have the same slope. Since the lines are described as parallel and the dotted line passes through \((0, 0)\), we can denote the slope of the dotted line as \(m_2\) which will be equal to \(m_1\) (the slope of the solid line). Thus, the equation of the dotted line can also be expressed in slope-intercept form: \[ y = m_2x + 0 \quad \text{or simplified to} \quad y = m_2x \]

To provide specific equations, we would need the value of the slope of these lines. However, without the slope value from the image, we can only express the equations in terms of their slopes.

Assuming a generic slope of \(m\) for both lines, the equations can be written as:

• For the solid line: \(y = mx + 3\)
• For the dotted line: \(y = mx\)

If you happen to have specific slope values, please provide them so I can give you the exact equations.