Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

# Points S(4, 10) and T(-2, -8)are on a line.Which equation represents a line that is perpendicular to this line and has the same y-intercept?

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• The line ST has slope (10 - - 8)/(4 - - 2) = 3.  The equation is y - 10 = 3(x - 4), or y = 3x +2.  It y-intercept is 2.  A line perpendicular to it has slope -1/3.  If that line also has the same y-intercept, then that line is y = -1/3(x - 6).

• You want the equation of a line that is perpendicular to the line represented by the two points that has the same y-intercept.

First, we need to put the original line into slope-intercept form to know its slope and y-intercept.  Starting with the general equation:

y = mx + b

Substitute the "x" and "y" values of the known points into the equation to get a system of two equations and two unknowns that we can solve:

(4, 10) and (-2, -8)

10 = m(4) + b and -8 = m(-2) + b

Solve both for b in terms of m:

10 = 4m + b and -8 = -2m + b

10 - 4m = b and -8 + 2m = b

Two expressions are each equal to "b", so both expressions are also equal to each other.  Solve for m:

10 - 4m = -8 + 2m

-6m = -18

m = 3

Now that we know "m", solve for "b":

b = 10 - 4m

b = 10 - 4(3)

b = 10 - 12

b = -2

So the slope of the original line is 3 and the intercept is -2.

The perpendicular line will have a negative-reciprocal slope to the original.  So that slope is -1/3.  The intercepts are to be the same, so the equation of the second line is:

y = (-1/3)x - 2

•    First to post  ...... Here are the hints.. you do the work....

****  it's sad  so many do all the work for you, instead of letting you do it for yourself... you won't learn that way  ****

Anyway, choose a Best Answer, but NOT because they Gave you the Answer...

1.  find  eqn of line thru S,T   use  y - y1 = m ( x - x1)

I used  x1 = 4    y1 = 10

2.  rewrite  eqn in  slope intercept  form... y = mx + b

3.  the perpendicular  has  the same y intercept... b,  only  m is different.

4.  Now  what do you remember about slopes for a perpendicular  ?  it is  negative  reciprocal of the other lines  slope.

5. Now you have  y = mx + b  for the perpendicular  line.