YES!!!
When neither 'x' nor 'y' are taised to any power/index/exponent. then it is a linear equation.
3x = 5y
5y = 3x
Divide both sides by '5'
y = (3/5)x + 0
In other words it is a straight line, through the origin (0,0) of gradient '3/5'.
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3X = 5Y
solve for Y
Y = 3/5X
this is by definition a linear equation solved. You can plat this straight line on a graph.
Solved for y: y=(3x-13)/5 Solved for x: x=(5y+13)/3
We cannot find out the y and x intercept for the equation 3x plus 5y equals -15 by a single equation . But , we can try a hit and trial method for the same . when x =0 y =-3. when y=0 x=-5.
From first equation, -y = 3x + 3. Substitute in second equation: -3x + 5(3x + 3) = -21 ie 12x = -36 so x = -3 and y = -(-9 + 3) = 6. Easier method: subtract first equation from second giving -4y = -24 so y = 6, this in first equation gives -6 = 3x + 3, ie 3x = -9 so x = -3
In order to graph this equation, you have to isolate y. 3x + 5y = -2 3x + 5y + 2 = 0 3x + 2 = -5y (3x+2)/-5 = y Now you can plug it into a graphing calculator. If you're graphing by hand, the equation you'll want to use is: (-3/5)x - (2/5) = y So the slope will be negative 3/5 and the y-intercept is -2/5.
If: 3x-5y = 25 Then: -5y = -3x+25 And: y = 3/5x-5 So: slope is 3/5 or 0.6 and the y intercept is -5