Graph the line with slope -1/2 passing through the point (1, 4).
Understand the Problem
The question asks to graph a line given its slope and a point it passes through. The slope is -1/2 and the point is (1, 4). We need to plot this line on a coordinate plane.
Answer
The line passes through points (1, 4) and (3, 3). The slope is $ -\frac{1}{2} $.
Answer for screen readers
The line passes through the points (1, 4) and (3, 3).
Steps to Solve
- Plot the given point
Plot the point (1, 4) on the coordinate plane. This is our starting point.
- Use the slope to find another point
The slope is given as $ -\frac{1}{2} $. Since slope is $\frac{\text{rise}}{\text{run}}$, a slope of $ -\frac{1}{2} $ means for every 2 units we move to the right (run), we move 1 unit down (rise).
- Apply the slope to the point
Starting from the point (1, 4), move 2 units to the right and 1 unit down. This gives us the new point $ (1+2, 4-1) = (3, 3) $.
- Draw a line through the two points
Draw a straight line that passes through the points (1, 4) and (3, 3). This line represents the equation with the given slope and passing through the given point.
The line passes through the points (1, 4) and (3, 3).
More Information
The line slopes downward from left to right, reflecting the negative slope.
Tips
A common mistake is to misinterpret the slope as $\frac{1}{2}$ instead of $-\frac{1}{2}$ and graph a line with a positive slope. Another common mistake is to add/subtract the run and rise in the wrong direction.
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