Question

What is the equation, in slope-intercept form, of the linethat is perpendicular to the given line and passes throughthe point (2, -1)?42O y = - 1x-1323Oy = - 2x - 3/33-22Oy=3x-3O y = 3x - 7-2

Answer 1

Given:

The point on the given line is (-4,4) and (-1,3).

The required line passes through the point (2,-1).

Required:

We need to find the equation, in slope-intercept form, of the line that is perpendicular to the given line and passes through the point (2, -1).

Step-by-step explanation:

Consider the formula for the slope.

`slope\text{ =}(y_2-y_1)/(x_2-x_1)`

`The\text{ s}lope\text{ of the given line, }m_1=(3-4)/(-1-(-4))`

`The\text{ s}lope\text{ of the given line, }m_1=(-1)/(-1+4)`

`The\text{ s}lope\text{ of the given line, }m_1=(-1)/(3)`

The required line is perpendicular to the given line.

The slope of the perpendicular line is negative reciprocal.

`m_2=The\text{ negative reciprocal of }m_1`

`m_2=The\text{ negative reciprocal of \lparen}-(1)/(3)\text{\rparen}`
`m_2=3`

Consider the slope -ntercept line equation.

`y=m_2x+b`

`Substitute\text{ }m_2=3\text{ in the equation.}`

`y=3x+b`

Substitute x = 2 and y =-1 in the equation to find the value of b since the line passes through the point (2,-1).

`-1=3(2)+b`

`-1=6+b`

`-1-6=b`
`b=-7`

`Substitute\text{ b =-7 in the equation }y=3x+b.`
`y=3x-7`

Final answer:

`y=3x-7`