Graph the line with the equation y = -2/5x - 2.
Understand the Problem
The question is asking to graph the line defined by the equation y = -\frac{2}{5}x - 2. This involves plotting points based on the equation and determining the slope and y-intercept to draw the line accurately.
Answer
The line is represented by points (0, -2) and (5, -4).
Answer for screen readers
The line is graphed through the points (0, -2) and (5, -4).
Steps to Solve
- Identify the slope and y-intercept
The equation of the line is given in slope-intercept form, $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. In this case, we have:
- Slope ($m$) = $-\frac{2}{5}$
- Y-intercept ($b$) = $-2$
- Plot the y-intercept
Locate the y-intercept on the graph. Since $b = -2$, plot the point (0, -2) on the y-axis.
- Use the slope to find another point
The slope $\frac{rise}{run} = -\frac{2}{5}$ means that for every 5 units you move to the right (positive direction on the x-axis), move down 2 units (negative direction on the y-axis).
Starting from the y-intercept (0, -2):
- Move 5 units right to (5, -2)
- Move down 2 units to (5, -4)
Plot the point (5, -4).
- Draw the line
With the points (0, -2) and (5, -4) plotted, draw a straight line through these points, extending it in both directions.
The line is graphed through the points (0, -2) and (5, -4).
More Information
The graph of the line follows the rule defined by its slope and y-intercept. The slope indicates that the line descends as you move from left to right, confirming that it has a negative slope, which means it tilts downwards.
Tips
- Forgetting to plot the correct y-intercept.
- Miscalculating the slope; remember that a negative slope means moving down as you move right.
- Not extending the line far enough or not using a ruler for straightness.
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