Answer
C. 7y - 2x = 21
Expalnation
You must know that for two lines to be parallel to each other, they must have the same slope.
The standard form of equation of a line is expressed as y = mx+c
m is the slope of the line
Comparing to the given equation y = 2/7x – 5, you will see that
m = 2/7
This means that the equation that will be parallel to this line must also have a slope of 2/7.
Fromm the option given, we need to find the equation that has a slopw of 2/7.
Looking at option A
7x - 2y = -2
First we must write this in standard form y = mx+c as shown
To do this, we need to make y the subject of the formula:
7x - 2y = -2
-2y = -2-7x
-2y = -7x-2
Divide through by -2
-2y/-2 = -7x/-2 -2/-2
y = 7/2x + 1
The slope of this line is 7/2, this shows that the line is not parallel to the given line since their slope are different
Let us look at option C:
7y - 2x = 21
Rewrite the equation
7y = 21 +2x
Divide through by 7
7y/7 = 21/7 + 2/7 x
y = 3 + 2/7 x
y = 2/7 x + 3
We can see that the slope of this line is also 2/7 which is equivalent to the slope of the given line.
Hence the equation of the line parallel to y = 2/7x – 5 is 7y - 2x = 21
