Answer:
-3/2
Step-by-step explanation:
3x+2y=14
3x+2y -14 =0
f(x,y)=3x+2y-14
fx =3
fy=2
dy/dx = -3/2
[tex]\displaystyle\frac{2}{3}[/tex]
Perpendicular lines are lines that meet at a right angle.
Slope of Perpendicular Lines
All perpendicular lines have the same relationship between the slopes. The slope of a perpendicular line will be the opposite reciprocal of the slope of the original line.
This means to find the slope of the line perpendicular to 3x + 2y = 14, we first need to find its slope. One of the easiest ways to do this is to convert the equation into slope-intercept.
Slope-Intercept Form
Slope-intercept form is given by y=mx+b, where m is the slope and b is the y-intercept. To go from standard form to slope-intercept, just solve for y.
First, subtract 3x
Then, divide by 2
This means that the slope of the given line is -3/2. Now we can take the opposite reciprocal. By flipping the fraction and changing the sign we get the slope 2/3. Thus, the slope of a line perpendicular to the given equation is 2/3.
