Me with this problem! i don't understand!

determine the equation of a line perpendicular to -6x+9y-12=0 with the same y-intercept as the line defined by -8x+2y-6=0

y = -3/2 x + 3

Step-by-step explanation:

If two lines' slopes multiply to get -1, they are perpendicular to each other.

In -6x+9y-12=0, find the slope by converting to slope-intercept form.

Isolate y:

-6x+9y-12=0

-6x+9y = 12

9y = 6x + 12

y = 6/9 x + 12/9

y = 2/3 x + 4/3

The slope in this line is 2/3.

To find the slope of a perpendicular line, find its negative reciprocal. The negative reciprocal is when you switch the top and bottoms numbers and multiply it by -1.

2/3 => -3/2

The slope of the perpendicular line is -3/2.

In -8x+2y-6=0, find the y-intercept by converting to slope-intercept form.

Isolate y:

-8x+2y-6=0

-8x + 2y = 6

2y = 8x + 6

y = 8/4 x + 6/2

y = 2x + 3

Slope-intercept form is y = mx + b, which b is the y-intercept.

The y-intercept is 3.

Substitute the slope and y-intercept values into the equation of a line in  slope-intercept form.

y = mx + b

y = -3/2 x + 3