Question
Using what you have learned in this lesson, describe how you would graph any line with the equation y = mx + b.
write it simple
write it simple
Answers
Answer
write it in scentence
Answered by
GPT-4o mini
To graph a line with the equation \( y = mx + b \), follow these simple steps:
1. **Identify the Slope (m)**: This is the number in front of \( x \). It shows how steep the line is and the direction it goes. A positive slope means the line goes up from left to right, and a negative slope means it goes down.
2. **Identify the Y-Intercept (b)**: This is the constant term. It tells you where the line crosses the y-axis (when \( x = 0 \)).
3. **Plot the Y-Intercept**: Start by marking the point on the graph where \( y = b \) (the y value when \( x = 0 \)).
4. **Use the Slope to Find Another Point**: From the y-intercept, use the slope to find a second point. For example, if the slope is \( \frac{2}{1} \), move up 2 units and right 1 unit from the y-intercept.
5. **Draw the Line**: Connect the two points with a straight line, extending it in both directions.
6. **Label the Line**: Optionally, label the line with its equation for clarity.
That's it! You now have a graph of the line represented by the equation \( y = mx + b \).
1. **Identify the Slope (m)**: This is the number in front of \( x \). It shows how steep the line is and the direction it goes. A positive slope means the line goes up from left to right, and a negative slope means it goes down.
2. **Identify the Y-Intercept (b)**: This is the constant term. It tells you where the line crosses the y-axis (when \( x = 0 \)).
3. **Plot the Y-Intercept**: Start by marking the point on the graph where \( y = b \) (the y value when \( x = 0 \)).
4. **Use the Slope to Find Another Point**: From the y-intercept, use the slope to find a second point. For example, if the slope is \( \frac{2}{1} \), move up 2 units and right 1 unit from the y-intercept.
5. **Draw the Line**: Connect the two points with a straight line, extending it in both directions.
6. **Label the Line**: Optionally, label the line with its equation for clarity.
That's it! You now have a graph of the line represented by the equation \( y = mx + b \).
Answered by
GPT-4o mini
To graph a line with the equation \( y = mx + b \), first identify the slope \( m \) and the y-intercept \( b \); then, plot the y-intercept on the graph where the line crosses the y-axis. Next, use the slope to determine a second point by moving up or down based on its value and to the right, starting from the y-intercept. After marking both points, connect them with a straight line extending in both directions, and optionally label the line with its equation for clarity.