Question

Write an equation for the line that passes through (4,10) and is perpendicular to the line 6x-3y=5​

Answer 1

Answer:

y =  $-\frac{1}{2}$x + 12

Step-by-step explanation:

Given expressions:

           Coordinates = (4,10)

  Equation of the line;  6x - 3y = 5

Unknown:

Equation of the line perpendicular = ?

Solution:

 A line perpendicular to the given one will have a negative inverse slope.

  Equation of any given line is expressed as:

              y  = mx + c

y and x are the coordinates

 m is the slope

 c is the intercept

             Now; re-write 6x-3y = 5 in the form y= mx + c and find the slope;

   6x - 3y = 5

          -3y = 5- 6x

            y = $-\frac{5}{3}$ + 2x

The slope of a perpendicular line will be $-\frac{1}{2}$

Also, let us find the y-intercept, c;

         y  = mx + c

         10 =  $-\frac{1}{2}$ x 4 + c

       10 = -2 + c

         c  = 12

The equation of the new line is ;

        y =  $-\frac{1}{2}$x + 12

Answer 2

Answer:

$y = - \frac{ 5}{3} x + ( - \frac{5}{3} )$

Step-by-step explanation:

-3y=5-6x

y=5-6x÷(-3)

y=(-5/3)+2x

y=2x-(5/3)

At y-intercept x is 0 and y is -(5/3)

Gradient m=10-(-5/3)÷(4-0)

=35/12

y=mx+c

10=(35/12)4+c

c=-(5/3)