Given an equation of a line, find equations for lines parallel or perpendicular to it going through specified points. Find the appropriate equations and points from the table below. Simplify your equations into slope-intercept form.
Y=-3x-6;(-1, 5) = Write the equation of a line parallel to the given line but passing through the given point.
Y= -1/3X-4;(-6,-3) = Write the equation of a line perpendicular to the given line but passing through the given point.
This is an example of the format that is wanted
Parallel and Perpendicular
For this week’s discussion I am going to find the equations of lines that are parallel or perpendicular to the given lines and which are passing through the specified point. First I will work on the equation for the parallel line.
The equation I am given is y = -? x + 2 The parallel line must pass through point (-6, -3)
I have learned that a line parallel to another line has the same slope as the other line, so now I know that the slope of my parallel line will be -?.
Since I now have both the slope and an ordered pair on the line, I am going to use the point-slope form of a linear equation to write my new equation.
y – Y1 = m(x – x1) this is the general form of the point-slope equation y – (-3) = -?[x – (-6)]
Substituting in my known slope and ordered pair y + 3 = -?x + (-?) 6
Simplifying double negatives and distributing the slope y = -?x – 4 – 3
Because (-?)6 = -4 and 3 is subtracted from both sides
y = -?x – 7the equation of my parallel line!
This line falls as you go from left to right across the graph of it, the y-intercept is 7 units below the origin, and the x-intercept is 10.5 units to the left of the origin.
Now I am ready to write the equation of the perpendicular line.
The equation I am given is y = -4x – 1
The perpendicular line must pass through point (0, 5)
I have learned that a line perpendicular to another line has a slope which is the negative reciprocal of the…