Find the equation of the line. Use exact numbers.
1 answer:
Answer:
y = x - 3
Step-by-step explanation:
Let the general equation of the line be y = ax + b
Note that the points (6,0) and (0,-3) lie on the line. That means, it should satisfy the equation of the line. We substitute the points on the equation of the line.
We would have:
From (2), we get: b = -3
From (1), we have -6a = b
Substituting b = -3, we get:
-6a = -3
⇒ a = 1/2
Therefore, the equation of the line would become: y = 1/2x - 3
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9514 1404 393
Answer:
(x, y, z) = (-3, -1, 3)
Step-by-step explanation:
Many graphing calculators can solve matrix equations handily. Here, we use a combination of methods.
Use the last equation to write an expression for z.
z = 4 -x +4y
Substitute this into the second equation:
y -4(4 -x +4y) = -13
y -16 +4x -16y = -13
4x -15y -3 = 0
In genera form, the first equation can be written as ...
3x +y +10 = 0
Now, the solution to these two equations can be found to be ...
x = (-15(10) -1(-3))/(4(1) -3(-15)) = (-150 +3)/(4+45) = -3 . . . using "Cramer's rule"
y = -(10 +3x) = -(10 -9) = -1 . . . . from the first equation
z = 4 -(-3) +4(-1) = 3 . . . . . . . . from our equation for z
The solution to the system is (x, y, z) = (-3, -1, 3).
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<em>Additional comment</em>
Written as an augmented matrix, the system of equations is ...