Decide whether the pair of lines is parallel, perpendicular, or neither.

5x+4y=10
4x+5y=3

y = -(5/4)x + 10/4

and
y = -(4/5)x + 3/5
not the same slope because -5/4 is not -4/5
not perpendicular because -(5/4)/-(4/5) is not -1 (it is +1)

Determine whether the two lines 5x + 4y=8 and 4x+5y=10 are parallel, perpendicular, or neither. Why?

To determine whether two lines are parallel, perpendicular, or neither, we can compare their slopes. The general form of a linear equation is "y = mx + b," where "m" represents the slope.

For the first equation, 5x + 4y = 10, we need to rewrite it in slope-intercept form:
4y = -5x + 10
y = (-5/4)x + (10/4)
y = (-5/4)x + 5/2

Comparing this equation to y = mx + b, we can see that the slope (m) of the first line is -5/4.

For the second equation, 4x + 5y = 3, we can rewrite it in slope-intercept form:
5y = -4x + 3
y = (-4/5)x + (3/5)

Comparing this equation to y = mx + b, we can see that the slope (m) of the second line is -4/5.

Now that we have both slopes, we can compare them:

If two lines have slopes that are the same, they are parallel.
If the slopes are negative reciprocals of each other (i.e., when you multiply them, the result is -1), the lines are perpendicular.
If neither of the above conditions is true, the lines are neither parallel nor perpendicular.

Let's compare the slopes in this case:
The slope of the first equation is -5/4.
The slope of the second equation is -4/5.

Multiplying these two slopes gives us:
(-5/4) * (-4/5) = 20/20 = 1

Since the product of the slopes is 1, which is not -1, we can conclude that the lines are neither parallel nor perpendicular.

Put both equations in the form of a straight line which is y = mx + b and determine m for each line. If m is the same, the lines are parallel.