Write an equation in slope-intercept form for the line that passes through (-5,3) and is perpendicular to the line described by y= 5x.

Question

Write an equation in slope-intercept form for the line that passes through (-5,3) and is perpendicular to the line described by y= 5x.

Answer 1

Hi Haley;

Write an equation in slope-intercept form for the line that passes through (-5,3) and is perpendicular to the line described by y= 5x.

The equation is in slope-intercept form...

y=mx+b

m is the slope.

b is the y-intercept, the value of y when x=0.

y=5x

Slope is 5

y-intercept is zero.  However, this will be a non-issue when establishing the perpendicular equation.

In such equation, the slope is -1/5.

y=(-1/5)x+b

Let's apply the point-slope formula...

(y-y₁)=m(x-x₁)

y-3=(-1/5)(x--5)

y-3=(-1/5)(x+5)

y-3=(-1/5)x-1

y=(-1/5)x+2

Answer 2

Given line y = 5x

compare with slope intercept line equation y = mx + b where m is slope

therefore slope of given line is 5

 

Slope of new line is perpedicular to given line

therefore its slope is - 1/5

 

equation of new line

 

y = -1/5x + b

since it passes through -5,3

 

3 = -1/5x(-5) + b

 

b = 2

 

equation of new line

 

y = -1/5 x + 2

Answer 3

 L1l : Y = 5X

 

 L2:   Y = -1/5 X +b    /passes through ( -5.3)

 

         3 = -1/5(-5) +b

 

         b = 3 - 1 = 2

 

      L2 : Y = -1/5 X + 2