Graph the line with slope -1/2 passing through the point (1, 4).
Understand the Problem
The problem asks us to graph a line on a coordinate plane. We are given the slope of the line, which is -1/2, and a point that the line passes through, which is (1, 4). To graph the line, we can use the point-slope form of a line. Alternatively we can use the slope to find another point and draw a line through those two points.
Answer
The line that passes through (1,4) and has a slope of $-\frac{1}{2}$.
Answer for screen readers
The line passes through (1,4) and has a slope of $-\frac{1}{2}$.
Steps to Solve
- Plot the given point
Plot the point (1, 4) on the coordinate plane 2. Use the slope to find another point
The slope is $-\frac{1}{2}$. This means for every 2 units we move to the right on the x-axis, we move 1 unit down on the y-axis. So, starting from the point (1, 4), we move 2 units to the right to $x = 1 + 2 = 3$, and 1 unit down to $y = 4 - 1 = 3$. This gives us the point (3, 3). 3. Draw the line
Draw a line that passes through the points (1, 4) and (3, 3). 4. Extend the line
Extend the line in both directions to fill the coordinate plane.
The line passes through (1,4) and has a slope of $-\frac{1}{2}$.
More Information
The equation of the line can be represented as $y = -\frac{1}{2}x+\frac{9}{2}$.
Tips
A common mistake is to misinterpret the slope. For example, a slope of $-\frac{1}{2}$ is often confused with a slope of $-2$ or $\frac{2}{1}$. Another common mistake is to misplot the given point or to make errors when counting the rise and run using the slope.
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