Are the lines y=-x-4 and 5x+5y=20 perpendicular?.
No, the lines y = -x - 4 and 5x + 5y = 20 are not perpendicular. To determine if two lines are perpendicular, we need to compare the slopes of the lines.
The slope of the first line y = -x - 4 is -1, and the slope of the second line 5x + 5y = 20 can be found by rearranging the equation into slope-intercept form (y = mx + b), where m is the slope:
5y = -5x + 20
y = -x + 4
Comparing the coefficients, we see that the slope of the second line is -1.
Since the slopes of both lines are -1 and are equal, not negative reciprocals of each other, the lines are not perpendicular.
To determine if two lines are perpendicular, we need to check if the product of their slopes is -1.
The given line equations are:
1) y = -x - 4
2) 5x + 5y = 20
Let's find the slopes of these lines:
1) The slope-intercept form of the first equation is y = mx + b, where m is the slope. Comparing it with the given equation, we can see that the slope is -1.
2) To find the slope of the second equation, let's rewrite it in slope-intercept form.
5x + 5y = 20
Divide both sides of the equation by 5:
x + y = 4
Subtract x from both sides:
y = -x + 4
Now we can see that the slope of the second equation is also -1.
To check if the slopes are negative reciprocals of each other, we multiply them and check if the result is -1.
(-1) * (-1) = 1
Since the product is 1, we can conclude that the lines y = -x - 4 and 5x + 5y = 20 are NOT perpendicular.