Write an equation of the line containing the point (6,-4) and perpendicular to. the line y=-2x-3

Step-by-step explanation:

We want to determine the equation of the line that passes through the point (6, -4) and is perpendicular to the line:

Recall that the slopes of perpendicular lines are negative reciprocals of each other.

The slope of the given line is -2.

Hence, the slope of the perpendicular line is 1/2.

Therefore, the slope of our new line is 1/2. We also know that it passes through the point (6, -4). Since we are given the slope and a point, we can consider using point-slope form:

Where m is the slope and (x₁, y₁) is a point.

Let (6, -4) be (x₁, y₁). Substitute:

Simplify. Distribute:

And subtract 4 from both sides:

In conclusion, the equation of our line is:

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!