Question
find the slope and y intercept to graph the equation f(x)=-2x+5
slope:
y- intercept:
graph the equation
slope:
y- intercept:
graph the equation
Answers
Answered by
GPT-4o mini
To find the slope and y-intercept of the linear equation \( f(x) = -2x + 5 \), we can identify these components from the equation, which is in the slope-intercept form \( f(x) = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
1. **Slope**: The coefficient of \( x \) in the equation \( f(x) = -2x + 5 \) is \(-2\). Therefore, the slope is:
\[
\text{slope} = -2
\]
2. **Y-Intercept**: The constant term in the equation is \( 5 \). Therefore, the y-intercept is:
\[
\text{y-intercept} = 5
\]
This means the graph will cross the y-axis at the point \( (0, 5) \).
### Graphing the Equation
To graph the equation, you can follow these steps:
1. **Plot the Y-Intercept**: Start by plotting the point \( (0, 5) \) on the graph.
2. **Use the Slope**: The slope of \(-2\) can be interpreted as "down 2 units for every 1 unit right". Starting from the point \( (0, 5) \):
- Move 1 unit to the right (to \( x = 1 \)).
- Move 2 units down (from \( y = 5 \) to \( y = 3 \)), arriving at the point \( (1, 3) \).
3. **Plot Another Point**: Plot the point \( (1, 3) \) on the graph.
4. **Draw the Line**: Connect the two points with a straight line and extend it in both directions.
### Summary
- **Slope**: -2
- **Y-Intercept**: \( (0, 5) \)
If you were to sketch this graph, it would be a straight line that slopes downward from left to right, starting at the point \( (0, 5) \) on the y-axis and passing through \( (1, 3) \).
1. **Slope**: The coefficient of \( x \) in the equation \( f(x) = -2x + 5 \) is \(-2\). Therefore, the slope is:
\[
\text{slope} = -2
\]
2. **Y-Intercept**: The constant term in the equation is \( 5 \). Therefore, the y-intercept is:
\[
\text{y-intercept} = 5
\]
This means the graph will cross the y-axis at the point \( (0, 5) \).
### Graphing the Equation
To graph the equation, you can follow these steps:
1. **Plot the Y-Intercept**: Start by plotting the point \( (0, 5) \) on the graph.
2. **Use the Slope**: The slope of \(-2\) can be interpreted as "down 2 units for every 1 unit right". Starting from the point \( (0, 5) \):
- Move 1 unit to the right (to \( x = 1 \)).
- Move 2 units down (from \( y = 5 \) to \( y = 3 \)), arriving at the point \( (1, 3) \).
3. **Plot Another Point**: Plot the point \( (1, 3) \) on the graph.
4. **Draw the Line**: Connect the two points with a straight line and extend it in both directions.
### Summary
- **Slope**: -2
- **Y-Intercept**: \( (0, 5) \)
If you were to sketch this graph, it would be a straight line that slopes downward from left to right, starting at the point \( (0, 5) \) on the y-axis and passing through \( (1, 3) \).