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

May 15, 2018

$y = - \frac{2}{7} x + 5$

Explanation:

$2 y = 7 x$ , rewrite as:

$y = \frac{7}{2} x$
The slope is $\frac{7}{2}$, the slope of perpendicular lines are negative reciprocal, thus the slope is$- \frac{2}{7}$, then the equation of the line is:

$y = - \frac{2}{7} x + 5$

May 15, 2018

$y = - \frac{2}{7} x + 5$

Explanation:

First find the slope of the given line which is

$2 y = 7 x$

solve for $y$

$y = \frac{7}{2} x$

here the coefficient of x is the slope

the slope is =$\frac{7}{2}$

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

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

$y = - \frac{2}{7} x + 5$

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

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Desmos is a great calculator to graph equations and functions

May 15, 2018

The line perpendicular to $2 y = 7 x$ is $z = - \frac{2}{7} x + 5$

Explanation:

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

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:

$2 y = 7 x \implies y = \frac{7}{2} x$
This means $a = \frac{7}{2}$, so we get $z = - \frac{2}{7} x + 5$ since the perpendicular should go through $\left(0 , 5\right)$.

Graphically we get: