Without plotting the functions, find the points of the graph y = -7x + 8, where the abscissa and ordinate are opposite numbers.
We need to find the points of the graph y = -7x + 8, where the abscissa and ordinate are opposite numbers, without performing the graphing of functions. To do this, we will compose and solve a linear equation.
So, the abscissa and ordinate must be opposite numbers:
y = -x.
We substitute functions instead of y = -x in the equations and solve the resulting linear equation in one variable.
-x = -7x + 8;
We group the terms with and without variables in different parts of the equation.
-x + 7x = 8;
6x = 8;
We are looking for an unknown factor:
x = 8: 6;
x = 1 1/3.
The point has coordinates (1 1/3; -1 1/3).
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