How to graph using slope-intercept form?
Understand the Problem
The question is asking for guidance on how to plot a graph using the slope-intercept form of a linear equation, which is typically expressed as y = mx + b, where m is the slope and b is the y-intercept.
Answer
To plot a graph using the slope-intercept form, identify the slope and y-intercept, plot the y-intercept, use the slope to find another point, then draw and label the line.
Answer for screen readers
To plot a graph using the slope-intercept form, identify the slope and y-intercept, plot the y-intercept, use the slope to find another point, then draw and label the line.
Steps to Solve
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Identify the slope and y-intercept Start by identifying the slope ($m$) and y-intercept ($b$) from the linear equation. For example, in the equation $y = 2x + 3$, the slope is $2$ and the y-intercept is $3$.
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Plot the y-intercept on the graph On a coordinate plane, plot the point where the line intersects the y-axis. This point is $(0, b)$. For our example, plot the point $(0, 3)$.
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Use the slope to find another point The slope $m$ shows the rise over run. For a slope of $2$, you rise $2$ units up for every $1$ unit you move to the right. From the point $(0, 3)$, move up $2$ units (to $y = 5$) and $1$ unit to the right (to $x = 1$), giving you the point $(1, 5)$.
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Draw the line Connect the two points you've plotted: $(0, 3)$ and $(1, 5)$. Extend the line in both directions, adding arrows to indicate that it goes on indefinitely.
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Label the axes and the line Make sure to label the x-axis and y-axis, as well as writing the equation of the line somewhere on the graph for clarity.
To plot a graph using the slope-intercept form, identify the slope and y-intercept, plot the y-intercept, use the slope to find another point, then draw and label the line.
More Information
The slope-intercept form is a convenient way to express linear equations and helps in quickly understanding the behavior of the line without needing to calculate additional points.
Tips
- Confusing slope with y-intercept and vice versa – remember, the slope $m$ affects how steep the line is, while $b$ is the point where the line crosses the y-axis.
- Forgetting to plot the y-intercept correctly – check that you correctly identify $(0, b)$ when plotting the first point.
