Write an equation of the line that passes through (2,−3) and is perpendicular to the line y=−2x−3.

An equation of the line that passes through points (2,−3) and is perpendicular to the line is equal to

Given the following equation:

First of all, we would determine the slope of the given equation:

Slope,  = -2

In Mathematics, the slopes of two lines are said to be perpendicular when the product of these slopes is equal to negative one (-1).

Mathematically, this is given by;

Substituting the value of , we have:

The standard form of an equation of line is given by the formula;

Where:

Substituting the points into the formula, we have;

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y = x - 4

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 2x - 3 ← is in slope- intercept form

with slope m = - 2

Given a line with slope m then the slope of a line perpendicular to it is

= - = - = , thus

y = x + c ← is the partial equation

To find c substitute (2, - 3) into the partial equation

- 3 = 1 + c ⇒ c = - 3 - 1 = - 4

y = x - 4 ← equation of perpendicular line

She plays 5 new songs for every 2 old ones.

If she plays 15 new songs, she will play 6 old songs.

15 + 6 = 21

thus, she played 21 songs altogether.