Question
Give the slope and the y-intercept of the line with the given equation. Then, graph the linear equation.
y equals negative one ninth x
Question content area bottom left
Part 1
Select the correct choice below and fill in any answer boxes within your choice.
A.
The slope is
enter your response here.
(Simplify your answer.)
B.
The slope is undefined.
y equals negative one ninth x
Question content area bottom left
Part 1
Select the correct choice below and fill in any answer boxes within your choice.
A.
The slope is
enter your response here.
(Simplify your answer.)
B.
The slope is undefined.
Answers
GPT-4o mini
To find the slope and the y-intercept of the given equation \( y = -\frac{1}{9}x \), we can compare it to the slope-intercept form of a linear equation, which is:
\[
y = mx + b
\]
where \( m \) is the slope and \( b \) is the y-intercept.
### Given Equation:
- \( y = -\frac{1}{9}x \)
### Identifying the Slope and Y-intercept:
- The slope \( m \) is \( -\frac{1}{9} \).
- The y-intercept \( b \) is \( 0 \) (since there is no constant added, it means the line crosses the y-axis at \( (0, 0) \)).
### Part 1:
A. The slope is \(-\frac{1}{9}\).
### Y-intercept:
The y-intercept can be explicitly stated as:
- The y-intercept is \( (0, 0) \).
### Graphing the Line:
1. Start by plotting the y-intercept at the point \( (0, 0) \).
2. From the y-intercept, use the slope to find another point. The slope of \(-\frac{1}{9}\) means that for every 9 units you move to the right (positive \( x \)), you move 1 unit down (negative \( y \)):
- From \( (0, 0) \) move right 9 units to \( (9, 0) \) and down 1 unit to \( (9, -1) \).
3. Plot the point \( (9, -1) \).
4. Draw a straight line through the points \( (0, 0) \) and \( (9, -1) \).
### Conclusion:
The final answer for slope is:
- The slope is \(-\frac{1}{9}\).
And you can visualize the line by plotting the points on a graph.
\[
y = mx + b
\]
where \( m \) is the slope and \( b \) is the y-intercept.
### Given Equation:
- \( y = -\frac{1}{9}x \)
### Identifying the Slope and Y-intercept:
- The slope \( m \) is \( -\frac{1}{9} \).
- The y-intercept \( b \) is \( 0 \) (since there is no constant added, it means the line crosses the y-axis at \( (0, 0) \)).
### Part 1:
A. The slope is \(-\frac{1}{9}\).
### Y-intercept:
The y-intercept can be explicitly stated as:
- The y-intercept is \( (0, 0) \).
### Graphing the Line:
1. Start by plotting the y-intercept at the point \( (0, 0) \).
2. From the y-intercept, use the slope to find another point. The slope of \(-\frac{1}{9}\) means that for every 9 units you move to the right (positive \( x \)), you move 1 unit down (negative \( y \)):
- From \( (0, 0) \) move right 9 units to \( (9, 0) \) and down 1 unit to \( (9, -1) \).
3. Plot the point \( (9, -1) \).
4. Draw a straight line through the points \( (0, 0) \) and \( (9, -1) \).
### Conclusion:
The final answer for slope is:
- The slope is \(-\frac{1}{9}\).
And you can visualize the line by plotting the points on a graph.