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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

  1. 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 $3$.

  2. 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 $(0, 3)$.

  3. 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 $(1, 5)$.

  4. 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.

  5. 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.
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