What is the slope, m, of the graph of this line? What is the y-intercept of the graph of this line? Graph the linear equation.
Understand the Problem
The question is asking for the slope of the given linear equation and the y-intercept, and also requires graphing the linear equation.
Answer
The slope is $m = \frac{1}{5}$ and the y-intercept is $(0, 3)$.
Answer for screen readers
The slope $m$ is $\frac{1}{5}$ and the y-intercept is the ordered pair $(0, 3)$.
Steps to Solve
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Identify the slope from the equation The equation is given as $y = \frac{1}{5}x + 3$. The slope $m$ is the coefficient of $x$, which is $\frac{1}{5}$.
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Determine the y-intercept of the graph The y-intercept is the constant term in the equation, which is where the line crosses the y-axis. In this case, it is $3$. We can express the y-intercept as the ordered pair $(0, 3)$.
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Summarize the slope and y-intercept We have found that the slope $m = \frac{1}{5}$ and the y-intercept is $(0, 3)$.
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Graph the linear equation To graph the equation, plot the y-intercept $(0, 3)$ on the coordinate plane. From there, use the slope $\frac{1}{5}$ to find another point. This means that for every $5$ units you move to the right (along the x-axis), you will move up $1$ unit (along the y-axis).
- Starting from $(0, 3)$, moving right $5$ units to $(5, 3)$ and then up $1$ unit gives us the point $(5, 4)$.
- Draw a straight line through the points $(0, 3)$ and $(5, 4)$ to complete the graph.
The slope $m$ is $\frac{1}{5}$ and the y-intercept is the ordered pair $(0, 3)$.
More Information
The slope indicates the steepness and direction of the line (a positive slope means the line rises as it moves to the right), while the y-intercept tells us where the line crosses the y-axis.
Tips
- Confusing the slope with the y-intercept. Remember, the slope is the coefficient of $x$, while the y-intercept is the constant.
- Miscalculating the slope when trying to find the rise over run. Ensure you interpret the slope correctly from the equation.
