Given an equation of a line, find equations for lines parallel or perpendicular to it going through...

Question

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 – 7 the 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 slope of the other line so the first thing I must do is find the negative reciprocal of –4.
The reciprocal of -4 is -¼, and the negative of that is – (-¼) = ¼.
Now I know my slope is ¼ and my given point is (0, 5). Again I will use the point-slope form of a linear equation to write my new equation.
y – y1 = m(x – x1) y – 5 = ¼ (x – 0) Substituting in the slope and ordered pair y – 5 = ¼ x The zero term disappears y = ¼ x + 5 Adding 5 to both sides of the equation The equation of my perpendicular line!
This line rises gently as you move from left to right across the graph. The y-intercept is five units above the origin and the x-intercept is 20 units to the left of the origin.
[The answers to part d of the discussion will vary with students’ understanding.]

005_bnmlapo-4eid2nst.docx

David · Accepted Answer

Sol: (1)  
    The equation is given by   3 6y x   . The parallel line must pass through 
point     1,5 .    
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 -3.  
 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.   
 1 1y y m x x   ,

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...

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