Answer:
y = -3/2 x + 3
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