Griffiths Allan
07/03/2023 · Senior High School
Slope of \( -\frac{1}{4} \) and contains \( (4,-3) \)
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Tutor-Verified Answer
Step-by-step Solution
To find the equation of a line with a slope of \( -\frac{1}{4} \) that passes through the point \( (4, -3) \), we can use the point-slope form of the equation of a line, which is given by:
\[
y - y_1 = m(x - x_1)
\]
where \( m \) is the slope, and \( (x_1, y_1) \) is the point the line passes through. Here, \( m = -\frac{1}{4} \), \( x_1 = 4 \), and \( y_1 = -3 \).
Substituting these values into the point-slope form:
\[
y - (-3) = -\frac{1}{4}(x - 4)
\]
This simplifies to:
\[
y + 3 = -\frac{1}{4}(x - 4)
\]
Next, we can distribute the slope on the right side:
\[
y + 3 = -\frac{1}{4}x + 1
\]
Now, we can isolate \( y \) by subtracting 3 from both sides:
\[
y = -\frac{1}{4}x + 1 - 3
\]
This simplifies to:
\[
y = -\frac{1}{4}x - 2
\]
Thus, the equation of the line with a slope of \( -\frac{1}{4} \) that passes through the point \( (4, -3) \) is:
\[
\boxed{y = -\frac{1}{4}x - 2}
\]
Quick Answer
The equation of the line is \( y = -\frac{1}{4}x - 2 \).
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