find the two equations of lines that are parallel and perpindicular to the lines with this eqaution. y=3x+9 how do u do this
That equation is in the form:
y = m x + b
m is the slope, and b is where the line hits the y axis where x = 0.
therefore the slope, m, is 3
any other line with sole 3 is parallel to your line, so for example
y = 3 x
or
y = 3 x + 459.73
or whatever. b does not matter for parallel, only m
Now for perpendicular, any line with
m' = -1/m
will be perpendicular to lines with slope m
if m = 3, then m' = -1/3
so for example
y = -x/3
will do
or
y = -x/3 + 75694.783
will do
Explain in words how to write an equation that is part one: parallel and then also part two: perpendicular to the equation y=2/3x-4 passing through the point (-2,-5). Write your answer in standard form.
Explain in words how to write an equation that is part one: parallel and then also part two: perpendicular to the equation y=2/3x-4 passing through the point (-2,-5). Write your answer in standard form
To find the equations of lines that are parallel and perpendicular to the given equation y = 3x + 9, we need to understand the relationship between their slopes.
The slope-intercept form of a line is given by y = mx + b, where m represents the slope of the line. Two lines are parallel if they have the same slope, and they are perpendicular if the product of their slopes is -1.
1. Finding the equation of a line parallel to y = 3x + 9:
Since the given line has a slope of 3, any line parallel to it will also have a slope of 3. To find the equation, we need a point on the line. Let's assume the point (x, y) to be (0, b) (where b is the y-intercept).
Using the point-slope form y - y1 = m(x - x1) with m = 3, x1 = 0, and y1 = b:
y - b = 3(x - 0)
y - b = 3x
y = 3x + b
Therefore, the equation of a line parallel to y = 3x + 9 is y = 3x + b.
2. Finding the equation of a line perpendicular to y = 3x + 9:
Since the given line has a slope of 3, the perpendicular line will have a slope that is the negative reciprocal of 3. The negative reciprocal of a number is found by inverting the number and changing its sign. Thus, the slope of the perpendicular line is -1/3.
Again, let's assume the point (x, y) to be (0, b) (where b is the y-intercept).
Using the point-slope form y - y1 = m(x - x1) with m = -1/3, x1 = 0, and y1 = b:
y - b = (-1/3)(x - 0)
y - b = (-1/3)x
y = (-1/3)x + b
Therefore, the equation of a line perpendicular to y = 3x + 9 is y = (-1/3)x + b.
Note: The y-intercept (b) is generally different for each line, depending on the specific point you choose or other given conditions.