5. Find the equation of a line given a line perpendicular which is y=2/5x-3 and a point (-1,-4)?

Question

Find the equation of a line given a line perpendiculat which is y=2/5x-3 and a point (-1,-4).

Answer 1

The slope of the perpendicular line is going to be -5/2.  Plug in your known point in the point-slope form of a line:

(y+4)=(-5/2)*(x+1)

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Answer 2

Since the slope of the original line is 2/5, the slope of a perpendicular line will be -5/2 (the opposite reciprocal).  You can use the y=mx+b formula to find the equation.  Plug in the slope (m), and the x and y from the point you're given (x,y):

-4 = (-5/2)(-1) + b

-4 = 5/2 +b

-8/2 = 5/2 +b

-13/2 =b

Now you have m and b.  So your equation is y= -5/2 x -13/2.

If you need it to be in standard form, then multiply everything by 2:

2y=-5x-13

5x+2y= -13

Alternatively, you can use point-slope form (less common, but easier in this case).  That's (y-y')=m(x-x')

You use the slope of -5/2, and you plug in the x and y to the x' and y'.

(y - -4) = -5/2 (x - -1)

(y+4)=-5/2(x+1)

multiply both sides by 2 to get rid of the fraction

2(y+4)=-5(x+1)  

Distrubute.

2y+8= -5x-5

Add 5x to each side, subtract 8 from each side.

5x +2y = -13

Answer 3

Try it yourself, not hard at all.

plug in the x and y coordinates.

Perpendicular lines are negative reciprocal of the other line so the new slope would be (-5/2)

The y intercept if most likely different so solve for that.

so it would be -4=(-5/2)(-1)+b

Solve for b, then plug back into y=mx+b formula, leaving y and x as variables, and plugging in the values of m(slope) and b(y intercept).

Answer 4

Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Perpendicular lines have slopes that are opposite reciprocals. Line y =(2/5)x - 3 has a slope of 2/5, so a line perpendicular to it has a slope of -5/2. Therefore, the equation of the line you are trying to find is y = (-5/2)x + b so far. Now solve for b by substituting the point (-1, -4) for x and y into the equation:

y = (-5/2)x + b

-4 = (-5/2)(-1) + b

-4 = 5/2 + b

-13/2 = b

ANSWER: y = (-5/2)x - 13/2