An equation of the line that passes through the given point and is parallel to the graph of the given equation
1 answer:
To construct the equations for these lines, we are going to use the point-slope formula, which is:
is the slope of the line
is a point on the line
1)
In this case, our point is (2, -1) and our line has a slope of 5. (Remember that the line is parallel, meaning that it has the same slope as the given line. Since the line is in the y = mx + b format, we could easily pick out the slope m as being 5.)
Thus, we can "plug in" what we know into our formula to find the equation of our line:
2)
We are going to do the same thing, except our point is now (0, -5) and our slope is now 9.
Our equations are:
1) y = 5x - 11
2) y = 9x - 5
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Answer:
<em>Cathy was born in 1980 and she was 18 years old in 1998</em>
Step-by-step explanation:
<u>Equations</u>
This is a special type of equations where all the unknowns must be integers and limited to a range [0,9] because they are the digits of a number.
Let's say Cathy was born in the year x formed by the ordered digits abcd. A number expressed by its digits can be calculated as
In 1998, Cathy's age was
And it must be equal to the sum of the four digits
Rearranging
We are sure a=1, b=9 because Cathy's age is limited to having been born in the same century and millennium. Thus
Operating
If now we try some values for c we notice there is only one possible valid combination, since c and d must be integers in the range [0,9]
c=8, d=0
Thus, Cathy was born in 1980 and she was 18 years old in 1998. Note that 1+9+8+0=18
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above
so we're really looking for the equation of a line whose slope is 1/2 and passes through (-4 , 1)