Determine whether the graphs of lines with the given Equations are Parallel,
Perpendicular or neither.
Eq#1 2X + 3Y = 4 and Eq#2 Y = - 2/3 X + 8
i am not going to solve the problem for you but i will tell you how to
first you have to convert both equations to y=mx+b form. You can do it by isolating the y variable to one side. If Y has a coeffienct then divide it by the coefficent and do the same thing on the other side. once u have that, now u have to look a the slopes. if the slopes are the same then the equations are parallel and if they are both negative reciprocal of one another then it it perpendicular. if they are neither of them then it is neither
To determine whether the graphs of the lines with the given equations are parallel, perpendicular, or neither, we can compare the slopes of the lines.
The slope-intercept form of a line is given by y = mx + b, where m represents the slope of the line. Thus, we need to rewrite the given equations in slope-intercept form.
Eq #1: 2X + 3Y = 4
To convert Eq #1 into slope-intercept form, isolate Y:
3Y = -2X + 4
Y = (-2/3)X + 4/3
The slope of Eq #1 is -2/3.
Eq #2: Y = -2/3X + 8
We can see that Eq #2 is already in slope-intercept form, and the slope is -2/3.
Now that we have the slopes of both lines, we can compare them.
If the slopes of two lines are equal, they are parallel.
If the slopes of two lines are negative reciprocals of each other (i.e., multiplying one slope by -1 and then inverting it gives the other slope), they are perpendicular.
If neither of these conditions is met, the lines are neither parallel nor perpendicular.
In this case, we can observe that the slopes of Eq #1 and Eq #2 are both equal to -2/3. Since the slopes are equal, the two lines are parallel.