write an equation for a line perpendicular to y=-3x+3 and passing through the point (-3,3)
To find the equation of a line perpendicular to y = -3x + 3 and passing through the point (-3, 3), we need to find the slope of the original line and then find the negative reciprocal to get the slope of the perpendicular line.
The original line has a slope of -3, so the perpendicular line will have a slope of 1/3.
Now we can use the point-slope form of a line to write the equation:
y - y1 = m(x - x1)
Plugging in the values, we get:
y - 3 = (1/3)(x - (-3))
Simplifying:
y - 3 = (1/3)(x + 3)
Distributing (1/3):
y - 3 = (1/3)x + 1
Now we can move the constant term to the other side:
y = (1/3)x + 1 + 3
Combining like terms:
y = (1/3)x + 4
So, the equation of the line perpendicular to y = -3x + 3 and passing through the point (-3, 3) is y = (1/3)x + 4.