Hodgson Lewis
06/02/2024 · Middle School
Write the point-slope form of the line that passes through \( (6,1) \) and is parallel to a line with a slope of -3. Include all of your work in your final answer. Type your answer in the box provided to submit your solution.
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To find the point-slope form of the line that passes through the point \( (6,1) \) and is parallel to a line with a slope of -3, we can use the point-slope form of a linear equation:
\[ y - y_1 = m(x - x_1) \]
where:
- \( (x_1, y_1) \) is the point through which the line passes, in this case, \( (6,1) \).
- \( m \) is the slope of the line, which is -3 for the line we are parallel to.
Substitute the values into the point-slope form:
\[ y - 1 = -3(x - 6) \]
Now, simplify the equation:
\[ y - 1 = -3x + 18 \]
\[ y = -3x + 19 \]
Therefore, the point-slope form of the line that passes through \( (6,1) \) and is parallel to a line with a slope of -3 is \( y = -3x + 19 \).
Quick Answer
The point-slope form of the line is \( y = -3x + 19 \).
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