Question

Write an equation of the line passing through the given point and satisfying the given condition. Give the equation (a) in slope-intercept form and (b) in standard form.
(8,6); perpendicular to 2x - y = 4
(a) Write the equation of the line in slope-intercept form.

Answer 1

Answer:

y =  -$\frac{1}{2}$x + 10

Step-by-step explanation:

To find the equation of a line that passes through the point (8,6) and perpendicular to the equation 2x - y = 4, we will follow the steps below:

first write the equation 2x - y = 4 in a standard form

we will find the slope of our equation using this equation

2x - y = 4

y = 2x -4

comparing the above with

y = mx  + c

m = 2

$m_{1}$$m_{2}$ = -1  ( slope of perpendicular equations)

2$m_{2}$ = -1

$m_{2}$  = -1/2

our slope m = -1/2

We can now go ahead and form our equation

$x_{1}$ =8   $y_{1}$ =6

y-$y_{1}$ = m (x-$x_{1}$)

y-6 = -$\frac{1}{2}$(x-8)

y-6 =  -$\frac{1}{2}$x + 4

y=  -$\frac{1}{2}$x+4+6

y =  -$\frac{1}{2}$x + 10