Chen Ball
03/15/2024 · Junior High School
Find an equation of the line having the given slope and containing the given point. Slope 6 ; through \( (2,1) \)
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Step-by-step Solution
To find the equation of a line given a slope and a point, we can use the point-slope form of the equation of a line, which is:
\[
y - y_1 = m(x - x_1)
\]
where \( m \) is the slope, and \( (x_1, y_1) \) is the point the line passes through.
Given:
- Slope \( m = 6 \)
- Point \( (x_1, y_1) = (2, 1) \)
Substituting these values into the point-slope form:
\[
y - 1 = 6(x - 2)
\]
Now, we can simplify this equation:
1. Distribute the slope on the right side:
\[
y - 1 = 6x - 12
\]
2. Add 1 to both sides to solve for \( y \):
\[
y = 6x - 12 + 1
\]
\[
y = 6x - 11
\]
Thus, the equation of the line is:
\[
\boxed{y = 6x - 11}
\]
Quick Answer
The equation of the line is \( y = 6x - 11 \).
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