|
Question 249951: Can someone please help me solve this
Exploration
a) Write a linear equation in two variables that is
satisfied by (3, 5).
b) Write another linear equation in two variables that is
satisfied by (3, 5).
c) Are your equations independent or dependent?
d) Explain how to select the second equation so that it will
be independent of the first.
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! a) When x=3, y=5.
y = 5/3x works.
,
b) We could pick the perpendicular line by setting the slope to the negative inverse of 5/3
y = -3/5x + b
.
We will have to solve 'b' to be sure the line goes through the point (3,5).
.
Substituting x=3 and y=5 (our known point), we have:
5 = -3/5(3) + b
.
Multiplying through we have...
5 = -9/5 + b
.
Adding 9/5 to both sides...
5 + 9/5 = b
.
Simplifying...
b = 5 + 1.8 = 6.8
.
So,
y = -3/5(x) + 6.8
.
c) Perpendicular lines are independent.
.
d) Any line that has a slope different from 5/3 that goes through the point (3,5) will be independent and consistent. it does not have to be perpendicular, just not parallel. A parallel line going through the point will be identical to the line itself, so it will be dependent.
.
Graphing the two equations is a good check:
|
|
|
| |
