SOLUTION: Write an equation of the line that passes through (4,3) and is (a) parallel and (b) perpendicular to the line shown. The two points on the line are (1,6) and (2,2). I have already

Algebra ->  Coordinate-system -> SOLUTION: Write an equation of the line that passes through (4,3) and is (a) parallel and (b) perpendicular to the line shown. The two points on the line are (1,6) and (2,2). I have already       Log On


   

Question 1205352: Write an equation of the line that passes through (4,3) and is (a) parallel and (b) perpendicular to the line shown. The two points on the line are (1,6) and (2,2). I have already tried y=-4x-13.
Found 4 solutions by MathLover1, josgarithmetic, MathTherapy, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
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The two points on the line are (1,6) and (2,2).
y=mx%2Bb where m=slope and b=y-intercept

first find a slope:
m=%282-6%29%2F%282-1%29=-4
y=-4x%2Bb+...use one point to calculate b
6=-4%2A1%2Bb+
6%2B4=b
b=10

equation of this line is
y=-4x%2B10

then, we need to find an equation of the line that passes through (4,3) and is
(a) parallel
parallel lines have same slope, so m=-4 and given point is (4,3)
use point slope formula
y-y1=-4%28x-x1%29
y-3=-4%28x-4%29
y-3=-4x%2B16
y=-4x%2B16%2B3
y=-4x%2B19


(b) perpendicular
perpendicular lines have a slopes negative+reciprocal to each other
if line has+m=-4, perpendicular line will have a slope m=-1%2F-4=1%2F4
so m=1%2F4 and given point is (4,3)
use point slope formula
y-3=%281%2F4%29%28x-4%29
y-3=%281%2F4%29x-%281%2F4%294
y=%281%2F4%29x-1%2B3
y=%281%2F4%29x%2B2




Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Perpendicular, the slope is negative reciprocal of the described and "shown"" line. Parallel, the slope is equal to the described and "shown" line.

According to the description, for your two points
y-2=%28%282-6%29%2F%282-1%29%29%28x-2%29
y-2=-4%28x-2%29
y=-4x%2B8%2B2
y=-4x%2B10------which should be the line with the two described points.


BUT pass through (4,3) and parallel to that given line?
3=-4%2A4%2Bb
3=-16%2Bb
b=19
So equation for this parallel line should be y=-4x%2B19.

Pass through (4,3) but perpendicular to given line?
3=%281%2F4%29%2A4%2Bb
b=2
So equation for this perpendicular line should be y=%281%2F4%29x%2B2.

Recheck for any mistakes.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Write an equation of the line that passes through (4,3) and is (a) parallel and (b) perpendicular to the line shown. The two points on the line are (1,6) and (2,2). I have already tried y=-4x-13.

All you need to create/form the parallel and perpendicular equations is the slope of the given line.
With given points, (1,6) = (x1, y1) and (2,2) = (x2, y2), slope (m) of "line shown" is,  

Using the point-slope formula, the "given" parallel-slope (m), - 4, and the given point (4, 3) we get 
parallel-equation,:  
                        y = - 4x + 19

Using the point-slope formula, the "given" perpendicular-slope (m), 1%2F4, and the given point (4, 3) we 
get perpendicular-equation,:

Answer by ikleyn(52800) About Me  (Show Source):
You can put this solution on YOUR website!
.

See the lessons

    - Find the slope of a straight line in a coordinate plane passing through two given points
    - Equation for a straight line having a given slope and passing through a given point
    - Solving problems related to the slope of a straight line
    - Equation for a straight line in a coordinate plane passing through two given points
    - Equation for a straight line parallel to a given line and passing through a given point
    - Equation for a straight line perpendicular to a given line and passing through a given point

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