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.
The point-slope form of a linear equation is given by the equation y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope of the line.
In this case, we are told that the line is parallel to a line with a slope of -3 and passes through the point (6, 1).
So the slope of the line we are looking for is also -3.
Using the point-slope form, we can substitute the values as follows:
y - 1 = -3(x - 6)
Now, let's simplify this equation:
y - 1 = -3x + 18
Adding 3x to both sides:
3x + y - 1 = 18
Adding 1 to both sides:
3x + y = 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 3x + y = 19.