are the lines y=-x-4 and 5x+5y=20 perpendicular?
To determine if two lines are perpendicular, we need to check if the product of their slopes is equal to -1.
The given line y = -x - 4 is in slope-intercept form, where the slope is the coefficient of x, which is -1.
The second line 5x + 5y = 20 needs to be rewritten in slope-intercept form.
First, we rearrange the equation:
5y = -5x + 20
Divide both sides by 5:
y = -x + 4
We can see that the slope of this line is also -1.
Now, let's check if the slopes are perpendicular by multiplying them:
-1 * -1 = 1
Since the product of the slopes is not equal to -1, the lines y = -x - 4 and 5x + 5y = 20 are not perpendicular.
To determine if two lines are perpendicular, we need to compare their slopes.
The given line equations are:
1. y = -x - 4
2. 5x + 5y = 20
To compare the slopes, we need to rewrite both equations in slope-intercept form (y = mx + b):
1. y = -x - 4 (already in slope-intercept form)
2. 5x + 5y = 20
Let's isolate y:
5y = -5x + 20
Divide both sides by 5:
y = -x + 4
Now we can compare the slopes, which are the coefficients of x in the slope-intercept form:
1. Slope of line 1: -1
2. Slope of line 2: -1
Since the slopes of both lines are the same (-1), the lines are parallel, not perpendicular.