To determine if the two lines are parallel, perpendicular, or neither, we can compare the slopes of the lines.
Given the equations:
3x - 4y = 13
8x + 6y = -15
First, let's put the equations into slope-intercept form, which is y = mx + b.
For the first equation, 3x - 4y = 13, let's isolate y:
-4y = -3x + 13
Divide by -4:
y = (3/4)x - (13/4)
For the second equation, 8x + 6y = -15, let's isolate y:
6y = -8x - 15
Divide by 6:
y = (-4/3)x - (5/2)
Now, we can compare the slopes. The slope of the first equation is 3/4, and the slope of the second equation is -4/3.
If the slopes of two lines are equal, then the lines are parallel.
If the slopes of two lines are negative reciprocals of each other (opposite signs and inverse values), then the lines are perpendicular.
Since 3/4 and -4/3 are not equal and not negative reciprocals, the two lines are neither parallel nor perpendicular.
Determine whether the two lines are parallel, perpendicular, or neither parallel nor perpendicular.
3x - 4y = 13
8x + 6y = -15
5 answers
Huh?
who says 3/4 and -4/3 are not negative reciprocals ?
They look perpendicular to me.
who says 3/4 and -4/3 are not negative reciprocals ?
They look perpendicular to me.
Apologies for any confusion. You are correct; 3/4 and -4/3 are indeed negative reciprocals of each other.
When two lines have slopes that are negative reciprocals of each other, they are perpendicular. Therefore, the two lines represented by the equations 3x - 4y = 13 and 8x + 6y = -15 are indeed perpendicular to each other.
When two lines have slopes that are negative reciprocals of each other, they are perpendicular. Therefore, the two lines represented by the equations 3x - 4y = 13 and 8x + 6y = -15 are indeed perpendicular to each other.
There are days when the Bot drives me crazy.
I apologize if my previous response caused any frustration. I'm here to help, so please let me know if there's anything specific you'd like assistance with.