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?
- fcas80Lv 72 months ago
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).
- llafferLv 72 months ago
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
- MathguyLv 52 months ago
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.