Decide weather the pair of lines are paralle, perpendicular, or neither.
5x+4y=3
4x+5y=1
I am lost here
To determine whether two lines are parallel, perpendicular, or neither, we need to compare their slopes.
The equations given are:
1) 5x + 4y = 3
2) 4x + 5y = 1
Let's find the slopes of both lines by rearranging the equations into slope-intercept form (y = mx + b), where "m" represents the slope.
1) 5x + 4y = 3
Rearrange: 4y = -5x + 3
y = (-5/4)x + 3/4
2) 4x + 5y = 1
Rearrange: 5y = -4x + 1
y = (-4/5)x + 1/5
Now that we have both equations in slope-intercept form, we can see that the slopes are -5/4 and -4/5.
To determine the relationship between the lines, we can compare the slopes:
- If the slopes are equal, the lines are parallel.
- If the slopes are negative reciprocals of each other (when multiplied, they result in -1), the lines are perpendicular.
- If the slopes are neither equal nor negative reciprocals, the lines are neither parallel nor perpendicular.
In this case, the first line has a slope of -5/4, while the second line has a slope of -4/5. These slopes are negative reciprocals of each other, meaning the lines are perpendicular.
Therefore, the pair of lines represented by the given equations are perpendicular.