Which is the Equation of a line perpendicular to the line
A 4x+3y=3
B 4x-3y=5
C 3x-4y=3
D 3x+4y=5
which line?
Hint: A&C and B&D are perpendicular
For Ax + By = C
the slope is -A/B
e.g. the slope of 3x - 4y = 3 is -3/-4 or 3/4
remember that if a given line has slope of k/l, then the perpendicular line will
have slope of - l/k ,
e.g. 6/7 vs -7/6
Use this information to answer your question
To determine the equation of a line that is perpendicular to a given line, we need to find the negative reciprocal of the slope of the given line.
Let's calculate the slope of each line and then find the negative reciprocal:
A: 4x + 3y = 3
First, rearrange the equation in the slope-intercept form (y = mx + b), where m represents the slope:
3y = -4x + 3
Divide each term by 3:
y = (-4/3)x + 1
The slope of line A is -4/3.
The negative reciprocal of -4/3 is 3/4.
B: 4x - 3y = 5
Rearrange the equation:
-3y = -4x + 5
Divide by -3:
y = (4/3)x - 5/3
The slope of line B is 4/3.
The negative reciprocal of 4/3 is -3/4.
C: 3x - 4y = 3
Rearrange the equation:
-4y = -3x + 3
Divide by -4:
y = (3/4)x - 3/4
The slope of line C is 3/4.
The negative reciprocal of 3/4 is -4/3.
D: 3x + 4y = 5
Rearrange the equation:
4y = -3x + 5
Divide by 4:
y = (-3/4)x + 5/4
The slope of line D is -3/4.
The negative reciprocal of -3/4 is 4/3.
Therefore, the line that is perpendicular to line A has a slope of 3/4,
the line that is perpendicular to line B has a slope of -3/4,
the line that is perpendicular to line C has a slope of -4/3,
and the line that is perpendicular to line D has a slope of 4/3.
If you would like the equation of the perpendicular line in point-slope form, you will need a point that the line passes through.