TKhalifa
contestada

Give the equation of the line, perpendicular to the line with equation y=2x+1, that passes
through the point (8,-2).

Respuesta :

Answer:

y = - [tex]\frac{1}{2}[/tex] x + 2

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 + 1 ← 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

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{2}[/tex] , thus

y = - [tex]\frac{1}{2}[/tex] x + c ← is the partial equation

To find c substitute (8, - 2) into the partial equation

- 2 = - 4 + c ⇒ c = - 2 + 4 = 2

y = - [tex]\frac{1}{2}[/tex] x + 2 ← equation of perpendicular line

blushingbees

Answer:

[tex]y=-\frac{1}{2}x+2[/tex]

Step-by-step explanation:

When two lines are perpendicular their slopes are negative reciprocals. So, if the slope of the first line is 2, then the slope of the line perpendicular to it is [tex]-\frac{1}{2}[/tex].

To find the y-intercept, input the slope and the given point (8, -2) into the equation y = mx + b and solve for b:

[tex]-2 = -\frac{1}{2}(8)+b[/tex]

-2 = -4 + b

2 = b

The y-intercept is 2.

Now that we know the slope and the y-intercept, we can write the equation:

[tex]y = -\frac{1}{2}x+2[/tex]

Hope this helps :)

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