Brooks Davies
11/08/2023 · Senior High School
Graph the following features: - Y-intercept \( =-1 \) Slope \( =\frac{2}{5} \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To graph the line with the given y-intercept and slope, follow these steps:
1. **Identify the y-intercept**: The y-intercept is the point where the line crosses the y-axis. In this case, the y-intercept is \( -1 \), which means the line crosses the y-axis at the point \( (0, -1) \).
2. **Use the slope**: The slope of a line is the ratio of the change in y to the change in x. In this case, the slope is \( \frac{2}{5} \), which means for every 5 units you move to the right (positive x-direction), you move up 2 units (positive y-direction).
3. **Plot the y-intercept**: Start by plotting the point \( (0, -1) \) on the graph.
4. **Use the slope to find another point**: From the y-intercept, move 5 units to the right (to the point \( (5, 0) \)) and then move up 2 units (to the point \( (5, 2) \)).
5. **Draw the line**: Now that you have two points, \( (0, -1) \) and \( (5, 2) \), draw a straight line through these points.
Here's a visual representation of the steps:
```
y
|
| *
| /
| /
| /
| /
| /
| /
|/
+----------------- x
0 5
```
The asterisk (*) represents the y-intercept \( (0, -1) \), and the line drawn through the points \( (0, -1) \) and \( (5, 2) \) represents the line with the slope \( \frac{2}{5} \).
Quick Answer
Plot the y-intercept at \( (0, -1) \). Use the slope \( \frac{2}{5} \) to find another point, such as \( (5, 2) \), and draw a line through these points.
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