25 POINTS!!! The equation y=470x represents the relationship between x, the time that a plane flies in hours, and y, the distanc
e the plane flies in miles for plane A. The table represents the relationship for plane B. Find the slope of the graph for each plane and the plane's rate of speed. Determine which plane is flying at a faster rate of speed. Look at the photo.
1 answer:
Answer:
Step-by-step explanation:
For plane A,
Equation that represents the relationship between time 'x' and distance 'y' is,
y = 470x
By comparing this equation with the slope-intercept form of the equation,
y = mx + b
m = slope = 470
b = 0
Here, slope represents the speed of plane A.
Therefore, speed of plane A = 470 mi per hour
For plane B,
From the given table,
Slope of the graph =
=
= 480
Speed of plane B = 480 miles per hour
Since, speed of plane B is more than plane A,
Plane B is flying faster.
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The first step in any problem is to look at what you are given. When solving systems of linear equations, it is often helpful to eliminate one or more of the variables by adding or subtracting a multiple of one equation with a multiple of another. It is convenient when at least one of the multipliers is 1.
Here, we can cancel the y-terms in the 2nd and 3rd equations simply by adding them together. This gives
... (5x +y -4z) +(-3x -y +5z) = (41) +(-45)
... 2x +z = -4 . . . . simplified
Likewise, we can add 3 times the second equation to the first to cancel y in that sum.
... 3(5x +y -4z) +(2x -3y +z) = 3(41) + (-1)
...15x +3y -12z +2x -3y +z = 123 -1
...17x -11z = 122 . . . . simplified
Now that we have 2 equations in x and z, we can go through the same process. We observe that the coefficient of z is +1 in the first equation and -11 in the second. The means we can cancel the z terms by adding 11 times the first equation to the second:
... 11(2x +z) +(17x -11z) = 11(-4) +122
...22x +17x = 78 . . . . . . simplify a little bit
... x = 78/39 = 2 . . . . . . divide by 39
From above, we find
... z = -4 -2x = -4 -2·2 = -8
... y = 41 -5x +4z = 41-5(2) +4(-8) = 41 -42 = -1
The solution is (x, y, z) = (2, -1, -8).
_____
The method of elimination used here will vary with the system of equations. If you want to employ a consistent method, you can use Cramer's Rule, Gaussian elimination, or matrix methods. Since you apparently don't mind help from technology, learning to do this on your graphing calculator can also be a good idea.
