Decide whether the pair of lines is parallel, perpendicular or neither.
5x+3y=4
3x+5y=5
If possible, convert each equation to the form:
y=mx+b
For equation one,
y=-(5/3)x+4
so m1=-(5/3)
Calculate similarly for m2.
if m1=m2, the lines are parallel.
if m1*m2=-1, the lines are perpendicular.
Otherwise, they are neither parallel nor perpendicular.
To determine whether the pair of lines is parallel, perpendicular, or neither, we need to compare their slopes. The general form of a linear equation is y = mx + b, where m represents the slope.
To find the slope of the first line, let's rewrite it in slope-intercept form by isolating y:
5x + 3y = 4
3y = -5x + 4
y = -(5/3)x + (4/3)
So, the slope of the first line is -5/3.
Now, let's find the slope of the second line by isolating y:
3x + 5y = 5
5y = -3x + 5
y = -(3/5)x + 1
So, the slope of the second line is -3/5.
Since the slopes of the two lines are different, i.e., -5/3 and -3/5, we can conclude that the pair of lines is neither parallel nor perpendicular.