How to graph an equation in slope-intercept form?
Understand the Problem
The question is asking for steps to graph an equation that is presented in slope-intercept form, which typically is written as y = mx + b, where m is the slope and b is the y-intercept.
Answer
Graphing the equation involves identifying the slope and y-intercept, plotting the intercept, using the slope to find another point, drawing the line, and labeling the graph.
Answer for screen readers
To graph an equation in slope-intercept form $y = mx + b$, identify the slope $m$ and the y-intercept $b$, plot the y-intercept, use the slope to find another point, draw the line, and label the graph.
Steps to Solve
- Identify the slope and y-intercept
From the slope-intercept form $y = mx + b$, identify the values for $m$ (slope) and $b$ (y-intercept). For example, in the equation $y = 2x + 3$, the slope $m$ is 2 and the y-intercept $b$ is 3.
- Plot the y-intercept
Start by plotting the point on the graph where the line crosses the y-axis. This point is given by the y-intercept $b$. For the example $y = 2x + 3$, you would plot the point (0, 3).
- Use the slope to find another point
The slope $m$ indicates how much the y-value increases or decreases for each unit increase in the x-value. If the slope is expressed as a fraction, such as $m = \frac{rise}{run}$, use this to find another point. For $m = 2$, you can interpret this as $2/1$, meaning from your y-intercept, move up 2 units and right 1 unit to find a second point.
- Draw the line
Once you have the y-intercept and the second point plotted on the graph, draw a straight line through these two points. This line represents the equation in slope-intercept form.
- Label the graph
Finally, label your axes and the graph itself, providing the equation of the line for clarity. Ensure the units are correct and clear for anyone reading the graph.
To graph an equation in slope-intercept form $y = mx + b$, identify the slope $m$ and the y-intercept $b$, plot the y-intercept, use the slope to find another point, draw the line, and label the graph.
More Information
Slope-intercept form is a useful way to express linear equations because it directly shows how steep the line is (slope) and where it starts on the y-axis (y-intercept). This form makes it easier to graph and analyze linear relationships.
Tips
- Neglecting to convert a fraction for the slope when interpreting rise and run—be sure to express the slope as a fraction to avoid confusion.
- Forgetting to check the signs of the slope and intercept—positive or negative values should be accurately reflected in the graph.
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