Write an equation in standard form of the line that contains the point (-3,4) and is
a. parallel to the line y=3x+4
b. perpendicular to the line y=3x+4
a) To find a line parallel to y = 3x + 4, we know that it will have the same slope of 3, since parallel lines have the same slope.
Using the point-slope formula, we can write the equation as:
y - 4 = 3(x - (-3))
Simplifying, we get:
y - 4 = 3(x + 3)
y - 4 = 3x + 9
3x - y = -13
So, the equation in standard form is 3x - y = -13.
b) To find a line perpendicular to y = 3x + 4, we know that the slope of this new line will be the negative reciprocal of 3, which is -1/3.
Using the point-slope formula, we can write the equation as:
y - 4 = (-1/3)(x - (-3))
Simplifying, we get:
y - 4 = (-1/3)(x + 3)
y - 4 = (-1/3)x - 1
(-1/3)x - y = -3
So, the equation in standard form is (-1/3)x - y = -3.