Question

 

homework help please?

Write an equation for the line that is perpendicular to the given line and that passes through the given point. Write the equation in slope-intercept form.

y = 1/2x - 8 ; (-1,4)

a.y = 2x + 6
b.y = 2x - 2
c.y = -2x + 2
d.y = -2x + 4

Answer 1

Slope-intercept form line equation is y = mx + c, where m is slope and c is y-intercept.

comapre the equation with slope-intercept form and find the slope. m = 1/2.

 

Perpendicular lines slopes are opposite reciprocals.

so slope of th eline = -1/m = -1/(1/2) = -2

The line equation is y = -2x + c

Find the y-intercept value by substituting (-1, 4) in the equation.

4 = -2 * -1 + c

4 = 2 + c

c = 2

 

The line equation is y = -2x + 2

Option C is right choice.

Answer 2

The equation  is y = 1/2 x - 8 and point is (-1, 4).

Above equation write in slope - intercept form y = m₁x + b.

y = 1/2 x - 8

Compare the equation with slope - intercept form y = m₁x + b.

So, m₁ = 1/2 and b = -8

Slope of the line perpendicular to the another line is negative receprocal of slope of the other line.

So, perpendicular slope m₂ = -1/m₁ = -1/(1/2) = -2.

You know the slope and a point on the line, so use the point - slope form with (x₁ ,y₁ ) = (-1, 4) to write equation of the line.

(y - y₁ ) = m₂(x - x₁ )

(y - 4) = -2(x - (-1))

(y - 4) = -2(x + 1)

Apply distributive property: a(b + c) = ab + ac.

y - 4 = (-2)x + (-2)1

y - 4 = (-2)x - 2

Add 4 to each side

y - 4 + 4 = (-2)x - 2 + 4

y  = -2x + 2

The equation is y  = -2x + 2.