MATH SOLVE

1 month ago

Q:
# Please help 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

Accepted Solution

A:

Answer:y = -3/2 x + 3Step-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 = 129y = 6x + 12y = 6/9 x + 12/9y = 2/3 x + 4/3The 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 => -3/2The 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 = 62y = 8x + 6y = 8/4 x + 6/2y = 2x + 3Slope-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 + by = -3/2 x + 3