Graph the line with slope -1/2 passing through the point (1, 4).
Understand the Problem
The question asks to plot a line on a graph given a specific slope and a point through which the line must pass. The slope is -1/2 and the point is (1,4).
Answer
The line passes through the points (1, 4) and (3, 3).
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 graph. This is our starting point.
- Interpret the slope
The slope is given as $ -\frac{1}{2} $. This means for every 2 units we move to the right (positive direction) on the x-axis, we must move 1 unit down (negative direction) on the y-axis.
- Find a second point using the slope
Starting from the point (1, 4), move 2 units to the right on the x-axis, which takes us to x = 3. Then move 1 unit down on the y-axis, which takes us to y = 3. This gives us a second point (3, 3).
- Draw the line
Draw a straight line that passes through both points (1, 4) and (3, 3). This line represents the equation with the given slope and passing through the specified point.
The line passes through the points (1, 4) and (3, 3).
More Information
The negative slope indicates that the line is decreasing as x increases.
Tips
A common mistake is to misinterpret the negative slope. Remember that a negative slope means that as x increases, y decreases. Another common mistake is incorrectly plotting the points or miscalculating the movement based on the slope.
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