Graph the line with slope 2 passing through the point (-4, -1).
Understand the Problem
The question asks to graph a line with a given slope and a point it passes through. We will use the point-slope form of a line to find the equation, and then graph the line based on the point and slope provided.
Answer
The line passes through (-4, -1) with a slope $m=2$.
Answer for screen readers
The graph of the line with slope 2 passing through the point (-4, -1) is a line that goes through the points (-4, -1) and (-3, 1).
Steps to Solve
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Plot the given point Plot the point (-4, -1) on the coordinate plane.
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Use the slope to find another point The slope is 2, which can be written as $\frac{2}{1}$. This means for every 1 unit we move to the right (run), we move 2 units up (rise). Starting from the point (-4, -1), move 1 unit to the right to x = -3 and 2 units up to y = 1. This gives us the new point (-3, 1).
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Draw the line Draw a straight line passing through the two points (-4, -1) and (-3, 1).
The graph of the line with slope 2 passing through the point (-4, -1) is a line that goes through the points (-4, -1) and (-3, 1).
More Information
The point-slope form of a line is given by $y - y_1 = m(x - x_1)$, where $m$ is the slope and $(x_1, y_1)$ is a point on the line. In this case, $m = 2$ and $(x_1, y_1) = (-4, -1)$. Plugging these values into the point-slope form, we get $y - (-1) = 2(x - (-4))$, which simplifies to $y + 1 = 2(x + 4)$. Further simplification gives $y + 1 = 2x + 8$, and finally, $y = 2x + 7$.
Tips
A common mistake is to misinterpret the slope. A slope of 2 means for every 1 unit increase in $x$, $y$ increases by 2 units. Another common mistake is making errors when plotting points on the coordinate plane, especially with negative numbers. Careful counting and attention to the signs are crucial to avoid this.
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