Question

Which equation represents a line which is parallel to the line y = 2/7x – 5?a) 7x - 2y = -2b) 2x + 7y = -42c) 7y - 2x = 21d) 7x + 2y = 10

Answer 1

c). 7y - 2x = 21.

Explanation:

Given line is y = 2/7x - 5

Parallel lines have the same slope.

The equation is in slope-intercept form so,

the slope of the given line is 2/7.

We need to convert the given choices to slope / intercept form:

a) 7x = 2y = -2

2y = 7x + 2

y = 7/2x + 1

- so, it's not this one.

b) 2x + 7y = -42

7y = -2x - 42

y = -2/7x - 6 . No.

c) 7y - 2x = 21

7y = 2x + 21

y = 2/7 + 3.

It's this one.

Answer 2

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