What is the equation of the line that passes through the point (-4, 1) and has a slope of -3/2?
Understand the Problem
The question is asking for the equation of a line that passes through a specified point and has a given slope. To solve it, we can use the point-slope form of the line equation: y - y1 = m(x - x1).
Answer
The equation of the line is $y = -\frac{3}{2}x - 5$.
Answer for screen readers
The equation of the line is: $$ y = -\frac{3}{2}x - 5 $$
Steps to Solve
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Identify the given values We have a point $(-4, 1)$ and a slope $m = -\frac{3}{2}$.
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Use the point-slope form The point-slope form is given by the equation: $$ y - y_1 = m(x - x_1) $$ Substituting in the values: $$ y - 1 = -\frac{3}{2}(x + 4) $$
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Distribute the slope Distributing the slope on the right side: $$ y - 1 = -\frac{3}{2}x - \frac{3}{2} \cdot 4 $$
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Calculate the product Calculating $-\frac{3}{2} \cdot 4 = -6$, so we have: $$ y - 1 = -\frac{3}{2}x - 6 $$
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Isolate y Add 1 to both sides to isolate $y$: $$ y = -\frac{3}{2}x - 6 + 1 $$ This simplifies to: $$ y = -\frac{3}{2}x - 5 $$
The equation of the line is: $$ y = -\frac{3}{2}x - 5 $$
More Information
This equation represents a straight line with a slope of $-\frac{3}{2}$, indicating it decreases as $x$ increases. The y-intercept is $-5$, meaning the line crosses the y-axis at that point.
Tips
- Forgetting to correctly distribute the slope when applying the point-slope formula can lead to incorrect results.
- Neglecting to simplify properly when isolating $y$.
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