Without an equality sign and not knowing the plus or minus values of 3y and 24 it can't be considered to be a straight line equation.
But if you mean: 4x+3y = 24 then the coordinates of the line are (6, 0) and (0, 8)
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To shift the graph of y = 4x + 7 down, you would subtract a constant from the equation. In this case, you would subtract 7 from the equation to shift it downward. The new equation would be y = 4x. This would shift the entire graph downward by 7 units along the y-axis.
If you mean y = -4x-6 then it is a straight line equation that can be graphed on the Cartesian plane
Since there are no "following" points, none of them.
There is no equation on the list you're showing that has the same graph as [ 4x + 8y = 12 ].
Most "quartic" functions will give you a M- or a w- shaped graph. Try y = x^4 -4x^2 for a W-shape, and y = -x^4 + 4x^2 for a M-shape.