6. Neither parallel nor Perpendicular
7. Parallel
8. Perpendicular
9. Parallel
Step-by-step explanation:
We have to compare the lopes of the lines to determine if the lines are parallel, perpendicular or neither of them.
If the slope of two lines i equal they are parallel and if the product of their slope is -1 then they are perpendicular.
6. The line containing points X(8, -3) and Y(-4, -6).
The line containing points R(1, 4) and S(-3, -3).
[tex]Slope\ of\ XY=\frac{y_2-y_1}{x_2-x_1}\\=\frac{-6-(-3)}{-4-8}\\=\frac{-6+3}{-12}\\=\frac{-3}{-12}\\=\frac{1}{4}[/tex]
[tex]Slope\ of\ RS = \frac{-3-4}{-3-1}\\=\frac{-7}{-4}\\=\frac{7}{4}[/tex]
Neither parallel nor perpendicular
7. The line containing points A(2, -1) and B(3,-4).
The line containing points C(1,6) and D(3, 0).
[tex]Slope\ of\ AB = \frac{-4+1}{3-2}\\=\frac{-3}{1}\\=\frac{-3}\\Slope\ of\ CD=\frac{0-6}{3-1}\\=\frac{-6}{2}\\=-3[/tex]
As the slopes of both lines are equal both lines are parallel.
8. y= 2x + 1
2y = -x-1
the given equation of line has to be converted in slope intercept form to find lope of both lines
Dividing the second equation by 2
[tex]\frac{2y}{2}=\frac{-x}{2} - \frac{1}{2}\\y=\frac{-x}{2}-\frac{1}{2}[/tex]
Both equations are in slope-intercept form
The co-effcients of are the slopes of the lines
So,
Slope of line 1: 2
Slope of line 2: -1/2
We can see that the product of both is -1
So the lines are perpendicular
9. 4x - y = 2
8x - 2y = -6
Converting both equations in slope intercept form
[tex]4x - y = 2\\4x-2=y[/tex]
Second equation
[tex]8x - 2y = -6\\8x=2y-6[/tex]
Dividing both equations by 2
[tex]y=4x-3[/tex]
The coefficients of x in both equations is which means the slopes of both lines are equal so the lines are parallel
Hence,
6. Neither parallel nor Perpendicular
7. Parallel
8. Perpendicular
9. Parallel
Keywords: Line, Slope
Learn more about equations of lines at:
#LearnwithBrainly
