decide whether the pair of lines is parrallel, perpendicular, or neither. 3x+4y+1 and 4x+3y=2
make them both equal to y and then graph on a graphing calculator and the result will help you answer this question
gluck
To determine whether the pair of lines is parallel, perpendicular, or neither, you can compare their slopes.
The given equations are:
Line 1: 3x + 4y + 1 = 0
Line 2: 4x + 3y = 2
To find the slope of each line, we need to rewrite the equations in slope-intercept form (y = mx + b), where m is the slope.
Line 1: 3x + 4y + 1 = 0
Rearranging the equation gives: 4y = -3x - 1
Dividing by 4 gives: y = (-3/4)x - 1/4
Comparing with the slope-intercept form (y = mx + b), the slope of Line 1 is -3/4.
Line 2: 4x + 3y = 2
Rearranging the equation gives: 3y = -4x + 2
Dividing by 3 gives: y = (-4/3)x + 2/3
Comparing with the slope-intercept form (y = mx + b), the slope of Line 2 is -4/3.
Since the slopes of Line 1 and Line 2 are not equal (-3/4 ≠ -4/3), we can conclude that the lines are neither parallel nor perpendicular.
To determine whether the pair of lines is parallel, perpendicular, or neither, we need to examine their slopes.
Let's rewrite the given equations in the slope-intercept form, which is y = mx + c, where m represents the slope:
The equation 3x + 4y + 1 can be rearranged as 4y = -3x - 1, or y = (-3/4)x - 1/4.
The equation 4x + 3y = 2 can be rearranged as 3y = -4x + 2, or y = (-4/3)x + 2/3.
Now we can determine the slopes for each line.
The slope of the first line is -3/4, as -3/4 is the coefficient in front of x in the rearranged equation.
The slope of the second line is -4/3, as -4/3 is the coefficient in front of x in the rearranged equation.
If the slopes of two lines are equal, the lines are parallel. If the slopes of two lines are negative reciprocals of each other (i.e., multiplying one slope by -1 and taking the reciprocal results in the other slope), the lines are perpendicular. If neither of these conditions are met, the lines are neither parallel nor perpendicular.
Let's check the slopes of the given lines: -3/4 and -4/3.
Since the given slopes are not equal, nor are they negative reciprocals of each other, we can conclude that the pair of lines is neither parallel nor perpendicular.