Question

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

Answer 1

Answer:

y = $\frac{1}{2}$ 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

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{-2}$ = $\frac{1}{2}$ , thus

y = $\frac{1}{2}$ x + c ← is the partial equation

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

- 3 = 1 + c ⇒ c = - 3 - 1 = - 4

y = $\frac{1}{2}$ x - 4 ← equation of perpendicular line

Answer 2

An equation of the line that passes through points (2,−3) and is perpendicular to the line is equal to $y=\frac{1}{2} x-4$

Given the following equation:

• $y=-2x-3$

• Points (x, y) = (2, -3)

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

Slope, $m_1$ = -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;

$m_1 \times m_2 = -1$  

Substituting the value of $m_1$, we have:

$m_1 \times m_2 = -1\\\\-2 \times m_2 = -1\\\\m_2 = \frac{1}{2}$

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

$y -y_1 =m(x-x_1)$

Where:

• x and y are the points.

• m is the slope.

Substituting the points into the formula, we have;

$y-y_1 =m(x-x_1)\\\\y-[-3] =\frac{1}{2} (x-2)\\\\y+3=\frac{1}{2} x -1\\\\y=\frac{1}{2} x-1 -3\\\\y=\frac{1}{2} x-4$

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