Which equation best represents the line perpendicular to 2y=7x if the y-intercept is b=5?

3 Answers
May 15, 2018

y=-2/7x+5

Explanation:

2y=7x , rewrite as:

y=7/2x
The slope is 7/2, the slope of perpendicular lines are negative reciprocal, thus the slope is-2/7, then the equation of the line is:

y=-2/7x+5

May 15, 2018

y = -2/7x+5

Explanation:

First find the slope of the given line which is

2y = 7x

solve for y

y = 7/2x

here the coefficient of x is the slope

the slope is =7/2

now the line that we need to find is perpendicular so its slope is
the reciprocal of 7/2 with a different sign so the slope of our line is =-2/7

the equation of the line that is perpendicular to 2y=7x is

y = -2/7x+5

+5 because is given in the question that it will intersect y-axis at 5


you can check you equation by graphing them using graph calculators like

https://www.desmos.com/calculator

Desmos is a great calculator to graph equations and functions

May 15, 2018

The line perpendicular to 2y=7x is z=-2/7x+5

Explanation:

We should know that if you have a line y=ax+b, then z=-1/ax+c is perpendicular to y, like in the following graph, where
y=-1/2x-1 is perpendicular to y=2x+3.

enter image source here

As this is a well known fact, I will take it as given. (See for instance http://www.bbc.co.uk/schools/gcsebitesize/maths/algebra/graphshirev1.shtml or http://www.coolmath.com/algebra/08-lines/14-perpendicular-lines-01

So let's write our line on the above form:

2y=7x => y=7/2x
This means a=7/2, so we get z=-2/7x+5 since the perpendicular should go through (0, 5).

Graphically we get:
enter image source here