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What is the slope of a line perpendicular to the line whose equation is 3x + 2y = 14. Fully simplify your answer.

Sagot :

Kari352idn

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

Wallameg000idn

Answer:

[tex]\displaystyle\frac{2}{3}[/tex]

Step-by-step explanation:

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.

  • 3x + 2y = 14

First, subtract 3x

  • 2y = -3x +14

Then, divide by 2

  • [tex]y=-\frac{3}{2}x+7[/tex]

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.

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