Answer:
Step-by-step explanation:
I hope I helped you^_^
The length of a rectangle is eight more than it’s width the perimeter is 48 inches what are the length and width?
1 answer:
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Answer:
(A)
(B)
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
Where "m" is the slope and "c" is the y-intercept.
By definition:
1. If the lines of the System of equations are parallel (which means that they have the same slope), the system has No solutions.
2. If the they are the same exact line, the System of equations has Infinite solutions.
Given the following System of Linear equations:
(A) Let's solve for "y" from the first equation:
You can notice that:
Then, in order make that the System has No solutions, the slopes must be the same, but the y-intercept must not.
Then, the values of "a" and "b" can be:
Substituting those values into the second equation and solving for "y", you get:
You can idenfity that:
Therefore, they are parallel.
(B) In order make that the System has Infinitely many solutions, the slopes and the y-intercepts must be the same.
Then, the values of "a" and "b" can be:
If you substitute those values into the second equation and then you solve for "y", you get:
You can identify that:
Therefore, they are the same line.
Hey there!
To start, the point slope form of an equation is as follows:
y-y1=m(x-x1)
y1= the value of the y value in the pair of coordinates
x1= the value of the x values in the pair of coordinates
m= the slope
Because you appear to already have a set of points to plug in for y1 and x1, all you need now is the slope.
As stated in the question, one of the coordinate points in which the equation passes through is the intersection of the lines 3x-y=3 and x+2y=15. **note: the reason you must find the intersection of the two points is because you need two sets of coordinate points in order to calculate the slope of the line that passes through the points.
To find the intersection of these lines, solve the equations for y and graph the equations:
3x-y=3
-y=-3x+3
y=3x-3
x+2y=15
2y=-x+15
y=-1/2x+15/2
(the graph is in the image below)
The point of intersection would be (3,6)
Now that you have two sets of coordinate points, (3,6) and (2,1), you can plug these values into your slope intercept equation to calculate your slope:
(y2-y1)/(x2-x1)
(1-6)/(2-3)
-5/-1
=5
Your slope, or m value would be 5.
Now that you have at least one set of coordinate points and a slope value, you can plug in either set of points and your slope to get either one of the following point slope equations as your answer:
y-1=5(x-2)
or
y-3=5(x-6)
Hope this helps! :)
To start, the point slope form of an equation is as follows:
y-y1=m(x-x1)
y1= the value of the y value in the pair of coordinates
x1= the value of the x values in the pair of coordinates
m= the slope
Because you appear to already have a set of points to plug in for y1 and x1, all you need now is the slope.
As stated in the question, one of the coordinate points in which the equation passes through is the intersection of the lines 3x-y=3 and x+2y=15. **note: the reason you must find the intersection of the two points is because you need two sets of coordinate points in order to calculate the slope of the line that passes through the points.
To find the intersection of these lines, solve the equations for y and graph the equations:
3x-y=3
-y=-3x+3
y=3x-3
x+2y=15
2y=-x+15
y=-1/2x+15/2
(the graph is in the image below)
The point of intersection would be (3,6)
Now that you have two sets of coordinate points, (3,6) and (2,1), you can plug these values into your slope intercept equation to calculate your slope:
(y2-y1)/(x2-x1)
(1-6)/(2-3)
-5/-1
=5
Your slope, or m value would be 5.
Now that you have at least one set of coordinate points and a slope value, you can plug in either set of points and your slope to get either one of the following point slope equations as your answer:
y-1=5(x-2)
or
y-3=5(x-6)
Hope this helps! :)