Decide weather the pair of lines are paralle, perpendicular, or neither.
5x+4y=3
4x+5y=1
I am lost here
for
Ax + By = C
the slope = - A/B
parallel lines have equal slopes
perpendicular lines have slopes that are opposite reciprocals of each other.
let me know what you concluded.
I would have to say paralle the way I did them but I am not to good at theis type of problem.
no
according to my formula the slope
for the 1st line = -5/4
for the 2nd line = -4/5
they are neither the same, nor are they opposite reciprocals.
So the answer is neither.
perhaps you are used to changing your equation to the form y = mx + b
1st --- > y = (-5/4)x + 3/4
2nd ---> y = (-4/5)x + 1/5
now compare the m values.
.... same conclusion.
Ok I understood that a little better. Thank you for your help.
To determine whether the pair of lines are parallel, perpendicular, or neither, you need to compare the slopes of the two lines.
A line's slope can be determined by putting its equation in slope-intercept form (y = mx + b), where "m" is the slope of the line.
Let's convert the given equations into slope-intercept form to find their slopes.
Equation 1: 5x + 4y = 3
Rearrange the equation to isolate "y":
4y = -5x + 3
y = (-5/4)x + 3/4
Thus, the slope of equation 1 is -5/4.
Equation 2: 4x + 5y = 1
Rearrange the equation to isolate "y":
5y = -4x + 1
y = (-4/5)x + 1/5
Therefore, the slope of equation 2 is -4/5.
Now, compare the slopes:
If two lines have the same slope, they are parallel.
If two lines have slopes that are negative reciprocals of each other (one slope is the negative reciprocal of the other), they are perpendicular.
If the slopes are neither the same nor negative reciprocals, the lines are neither parallel nor perpendicular.
In this case, the slope of equation 1 is -5/4, and the slope of equation 2 is -4/5. The slopes are not the same, nor are they negative reciprocals of each other. Hence, the pair of lines are neither parallel nor perpendicular.