Question

What is the equation, in slope-intercept form, of the line

that is perpendicular to the given line and passes through
the point (2, -1)?
y=- 2x - 2 / 2
y=- 2x - 5 / 5
y = 3x - 3
y = 3x - 7

Answer 1

Given:

Given that the graph of the equation of the line.

The line that is perpendicular to the given line and passes through the point (2,-1)

We need to determine the equation of the line perpendicular to the given line.

Slope of the given line:

The slope of the given line can be determined by substituting any two coordinates from the line in the slope formula,

`m=(y_2-y_1)/(x_2-x_1)`

Substituting the coordinates (-1,3) and (2,2), we get;

`m_1=(2-3)/(2+1)`

`m_1=-(1)/(3)`

Thus, the slope of the given line is
`m_1=-(1)/(3)`

Slope of the perpendicular line:

The slope of the perpendicular line can be determined by

`m_2=-(1)/(m_1)`

Substituting
`m_1=-(1)/(3)`, we get;

`m_2=-(1)/(-(1)/(3))`

simplifying, we get;

`m_2=3`

Thus, the slope of the perpendicular line is 3.

Equation of the perpendicular line:

The equation of the perpendicular line can be determined using the formula,

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

Substituting
`m=3` and the point (2,-1) in the above formula, we have;

`y+1=3(x-2)`

`y+1=3x-6`

`y=3x-7`

Thus, the equation of the perpendicular line is
`y=3x-7`

Hence, Option d is the correct answer.