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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=
.

2 answers

To determine the equations of the two lines, we can derive them based on the information given:

  1. Solid Line: It intersects the y-axis at the point (0, 3). This means that when \( x = 0 \), \( y = 3 \). Therefore, the equation of the solid line can be written in the intercept form as:

    \( y = mx + 3 \)

    where \( m \) is the slope. However, the slope is not specified for this solid line, so we cannot provide a specific numerical value for it. Therefore, the equation simplifies to:

    Equation of the solid line: \( y = mx + 3 \)

  2. Dotted Line: It passes through the point (0, 0), which means it goes through the origin. The general form for a line through the origin is:

    \( y = mx \)

    where \( m \) again represents the slope. The specific slope is not provided for this dotted line as well, so it remains as:

    Equation of the dotted line: \( y = mx \)

Thus, the slope for both lines needs to be specified for complete equations, but based on the information given, we can conclude:

  1. The equation of the solid line is: \( y = mx + 3 \)
  2. The equation of the dotted line is: \( y = mx \)

Without numeric values for the slopes, you would just input the generic equations as provided. If you know or can deduce the slopes from the lines' angles, please provide that information for more precise equations.