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The distance between both lines is 2.24 units
Step-by-step explanation:
There is no straight method to find the distance between two lines. The distance can be found out by finding a point on one line and then finding the distance of that point from the other line. The y-coordinate of point is obtained by putting any value of x in equation . The x and y combined give us the point.
Given
We have to find the distance of this point from y=2x+5
The formula for finding distance of a point (x,y) from a line is:
A=2
B=-1
C=5
Putting the values in the formula
Rounding off will give: 2.24 units
The distance between both lines is 2.24 units
Keywords: Equations of lines
Learn more about distance in lines at:
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To expand two terms such as these, we can use the method called FOIL (stands for First, Outer, Inner, Last). Here is what I mean:
We have two terms: (x - 2)(x - 1)
We should first multiply the First two terms of each term in order to complete the F stage:
(x)*(x) =
So then, we take the two outer terms and multiply them together to complete the O stage:
(x)*(-1) = -x
So far we have two things that we have calculated; at the end of the FOIL process we will have four.
To keep going with the FOIL, we now multiply the two inner terms to complete the I stage:
(-2)*(x) = -2x
Last but not least, we need to complete the L stage - so we multiply the two last terms of each term:
(-2)*(-1) = 2
Now that we have our four terms, let us add them together and combine like terms:
Since -x and -2x both have the x portion in common and they are added together, we can add them to create one single term:
-x + (-2x) = -3x
So now that we have our terms completed, we can combine into one polynomial equation:
or 
We have two terms: (x - 2)(x - 1)
We should first multiply the First two terms of each term in order to complete the F stage:
(x)*(x) =
So then, we take the two outer terms and multiply them together to complete the O stage:
(x)*(-1) = -x
So far we have two things that we have calculated; at the end of the FOIL process we will have four.
To keep going with the FOIL, we now multiply the two inner terms to complete the I stage:
(-2)*(x) = -2x
Last but not least, we need to complete the L stage - so we multiply the two last terms of each term:
(-2)*(-1) = 2
Now that we have our four terms, let us add them together and combine like terms:
Since -x and -2x both have the x portion in common and they are added together, we can add them to create one single term:
-x + (-2x) = -3x
So now that we have our terms completed, we can combine into one polynomial equation: