When I solved these two equation: 3x+4y=8
4x+3y=4
I found that neither of the two lines was perpendicular or parallel.
Is this correct?
Thanks.
To determine whether the two lines represented by the given equations are perpendicular, parallel, or neither, we can compare their slopes.
The general form of a linear equation is y = mx + b, where m represents the slope of the line.
The slope-intercept form of a linear equation is also commonly used, which is y = mx + b, where m represents the slope and b represents the y-intercept.
In order to find the slopes of the given equations, we can rewrite them in slope-intercept form. Let's start with the first equation:
3x + 4y = 8
To rewrite this equation in slope-intercept form, isolate the y variable:
4y = -3x + 8
y = (-3/4)x + 2
From this equation, we can see that the slope of the first line is -3/4.
Now, let's rewrite the second equation in slope-intercept form:
4x + 3y = 4
To isolate the y variable:
3y = -4x + 4
y = (-4/3)x + 4/3
From this equation, we can see that the slope of the second line is -4/3.
Since the slopes of the two lines, -3/4 and -4/3, are neither equal (which would make the lines parallel) nor negative reciprocals (which would make the lines perpendicular), we can conclude that the two lines given by the equations "3x + 4y = 8" and "4x + 3y = 4" are indeed neither parallel nor perpendicular to each other.
Thus, your conclusion is correct.