Which equation, when solved, results in a different value of x than the other three?
2 answers:
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To write the system we need the slope of each line and at least one point on the line. The two lines to consider will be the lines connecting the location of each plane to the airport they are flying to. It is also worth noting that the coordinates of the airport represent the point of intersection of the two lines and thus the solution to the system.
1. slope of the line connecting airplane one and the airport: m = 2 you can see this clearly if you graph the two points. From airplane 1 location we rise 8 units and move to the right 4 units to get to the airport. Slope is defined as rise over run: so 8 divided by 4 = 2(the slope) Now substitute the slope and the point (2,4) into point-slope form of a line:
y - 4 = 2(x -4) the standard form of this equation is 2x - y = 0
2. slope of the line connecting airplane 2 and the airport: m = -
To find this slope, simply observe the vertical change of down 3 and a horizontal shift of right 9 from the airport to airplane 2. Now substitute this slope and and the point (15,9) into point-slope form of a line:
y - 9 =
(x - 15) the standard form of this equation is:
x + 3y = 42
Let's write the system:
2x - y = 0
x + 3y = 42
Multiply the first equation by 3 to get the new system
6x - 3y = 0
x + 3y = 42 add these two equations to get an equation in terms of x
7x = 42 thus x = 6 and substituting this value into 2x - y = 0 we see y = 12
In other words, we have proven that the location of the airport is in fact the solution to our system.
PS: You just have to do a little algebra to get from point-slope form of the two equations to standard form. I did not show this process, but if you need it just let me know... thanks
1. slope of the line connecting airplane one and the airport: m = 2 you can see this clearly if you graph the two points. From airplane 1 location we rise 8 units and move to the right 4 units to get to the airport. Slope is defined as rise over run: so 8 divided by 4 = 2(the slope) Now substitute the slope and the point (2,4) into point-slope form of a line:
y - 4 = 2(x -4) the standard form of this equation is 2x - y = 0
2. slope of the line connecting airplane 2 and the airport: m = -
y - 9 =
x + 3y = 42
Let's write the system:
2x - y = 0
x + 3y = 42
Multiply the first equation by 3 to get the new system
6x - 3y = 0
x + 3y = 42 add these two equations to get an equation in terms of x
7x = 42 thus x = 6 and substituting this value into 2x - y = 0 we see y = 12
In other words, we have proven that the location of the airport is in fact the solution to our system.
PS: You just have to do a little algebra to get from point-slope form of the two equations to standard form. I did not show this process, but if you need it just let me know... thanks
Answer:
-3/2
Step-by-step explanation:
Let x be the missing number
- x*
=
- x =
*
inverse 14/25 since it's a fraction
- x =
- x =
write 75 as 25*3 and -28 as -4*7 to simplify
- x =
-4 is left on the top and 6 = 3*2
- x =
- x=
The cost to rent the canoe for 7 hours is $ 104
<em><u>Solution:</u></em>
At eagle bay it cost $12 per hour to rent a Canoe
Nate and his friends rented a canoe for 4 hours and paid $68
Let "x" be the number of hours rented
We can solve use the point slope equation
Where, "m" is the rate of change
is the sample point
From given,
m = 12
Therefore,
Thus the linear equation is found
Here, "y" represents the amount paid for "x" hours
<em><u>Find the cost to rent the canoe for 7 hours</u></em>
Substitute x = 7 in linear equation
y = 12(7) + 20
y = 84 + 20
y = 104
Thus cost to rent the canoe for 7 hours is $ 104
Answer:
Intercepts at (-1, 0) and (0, 1).
Step-by-step explanation:
The double intercept form for the equation of a line is
ax + by = 1
-1 = -y + x
<em> y = 0 </em>
<em> </em>x = -1 Multiply each side by -1
-x = 1
The <em>x-intercept</em> is at (-1, 0).
=====
<em> x = 0 </em>
-1 = -y Multiply each side by -1
y = 1
The <em>y-intercept</em> is at (0, 1).
=====
The graph (see below) is a straight line passing through the points (-1, 0) and (0, 1).
