Question
Writing Simultaneous Linear Equations Practice
Complete this assessment to review what you’ve learned. It will not count toward your grade.
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Question
Use the image to answer the question.
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.
Answers
GPT-4o mini
To write the equations for the system of linear equations being described, we need to analyze the details provided.
1. **Identifying the solid line**:
- The solid line intersects the y-axis at the point (0, 3), which means the y-intercept (b) is 3.
- Since the solid line is one of the equations and is described as parallel to another line, both lines will have the same slope (m). However, we need the slope to write the full equation.
Let's denote the equation of the solid line as:
\[
y = mx + 3
\]
where \(m\) is the slope of the line.
2. **Identifying the parallel line**:
- The other line is stated to be parallel to the first. Since parallel lines have the same slope, it will also have the form:
\[
y = mx + b_1
\]
Here, \(b_1\) is the y-intercept of the parallel line. Since you mentioned it is upward sloping, \(m\) must be a positive value.
3. **Dotted line through (0, 0)**:
- The dotted line passes through the origin (0, 0). The equation of a line passing through the origin has the form:
\[
y = mx
\]
where \(m\) is the slope, which may or may not be the same as the other lines, but if they are parallel to the solid line, it will also have the same slope.
In summary, we need to finalize the slope (m). However, without the exact numerical slope provided in your description, the two equations can be generalized as:
1. The solid line:
\[
y = mx + 3
\]
2. The parallel line:
\[
y = mx + b_1
\]
3. The dotted line:
\[
y = mx
\]
If you can provide the slope or any specific values for \(b_1\), we can finalize these equations!
1. **Identifying the solid line**:
- The solid line intersects the y-axis at the point (0, 3), which means the y-intercept (b) is 3.
- Since the solid line is one of the equations and is described as parallel to another line, both lines will have the same slope (m). However, we need the slope to write the full equation.
Let's denote the equation of the solid line as:
\[
y = mx + 3
\]
where \(m\) is the slope of the line.
2. **Identifying the parallel line**:
- The other line is stated to be parallel to the first. Since parallel lines have the same slope, it will also have the form:
\[
y = mx + b_1
\]
Here, \(b_1\) is the y-intercept of the parallel line. Since you mentioned it is upward sloping, \(m\) must be a positive value.
3. **Dotted line through (0, 0)**:
- The dotted line passes through the origin (0, 0). The equation of a line passing through the origin has the form:
\[
y = mx
\]
where \(m\) is the slope, which may or may not be the same as the other lines, but if they are parallel to the solid line, it will also have the same slope.
In summary, we need to finalize the slope (m). However, without the exact numerical slope provided in your description, the two equations can be generalized as:
1. The solid line:
\[
y = mx + 3
\]
2. The parallel line:
\[
y = mx + b_1
\]
3. The dotted line:
\[
y = mx
\]
If you can provide the slope or any specific values for \(b_1\), we can finalize these equations!