Brooks Davies
11/08/2023 · Senior High School

Graph the following features: - Y-intercept \( =-1 \) Slope \( =\frac{2}{5} \)

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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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