Final Answer:
The equation of the line that passes through the point (-5,5) and is perpendicular to y = -3x + 1 in point slope form is y = (1/3)x + 20/3.
Step-by-step explanation:
Sure, let's find the equation of the line that passes through the point (-5,5) and is perpendicular to the line with the equation y = -3x + 1.
When two lines are perpendicular, the slope of one line is the negative reciprocal of the slope of the other. The slope (m) of the given line y = -3x + 1 is -3. The slope of the line perpendicular to it will therefore be the negative reciprocal of -3, which is 1/3.
The point-slope form of the equation of a line is given by:
y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line.
Here, we have the slope m = 1/3 and the point (x₁, y₁) = (-5,5).
Now place these values into the point-slope form:
y - 5 = (1/3)(x - (-5))
Simplify the equation:
y - 5 = (1/3)(x + 5)
Distribute the 1/3:
y - 5 = (1/3)x + (1/3) * 5
y - 5 = (1/3)x + 5/3
Now we can add 5 to both sides to solve for y:
y = (1/3)x + 5/3 + 15/3
y = (1/3)x + 20/3
Thus, the equation of the line that passes through the point (-5,5) and is perpendicular to the line y = -3x + 1 in point-slope form is:
y = (1/3)x + 20/3