The lines having equations 4y=2x-4 and y=-2x+9 are perpendicular, 2y=4x+4 and y=-2x-2 come in case of neither, y=2x+4 and 2y=4x-7 are parallel.
Given three pairs of equations which are as under:
1) 4y=2x-4 and y=-2x+9
2) 2y=4x+4 and y=-2x-2
3) y=2x+4 and 2y=4x-7.
We are required to find whether the lines having those equations are perpendicular, parallel or come in case of neither.
We have to find the slope of individual equations and if the slopes are equal then they will be parallel , if the product of the slopes comes out to be -1 then they will be perpendicular.
The general form of slope intercept form is y=mx+c in which m is the slope.
Taking first pair.
4y=2x-4--------1
y=-2x+9---------2
Taking 1
y=2/4 x-4/4
y=x/2-1 (Slope is 1/2)
Taking 2
y=-2x+9 (Slope is -2)
Product of slopes=1/2 *(-2)
=-1
So they are perpendicular lines.
Taking second pair.
2y=4x+4---------3
y=-2x-2-----------4
Taking 3
y=4/2 x+4/2
y=2x+2 (Slope is 2)
Taking 4
y=-2-2 (Slope is -2)
Neither the slopes are equal and their product is also -4 so they come in the case of neither.
Taking third pair.
y=2x+4--------5
2y=4x-7-------6
Taking 5
y=2x+4 (Slope is 2)
Taking 6
y=4/2 x-7/2
y=2x-7/2 (Slope is 2)
Because the slopes of both the equations are equal,they are parallel lines.
Hence the lines having equations 4y=2x-4 and y=-2x+9 are perpendicular, 2y=4x+4 and y=-2x-2 come in case of neither, y=2x+4 and 2y=4x-7 are parallel.
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