Find a formula for a linear function y = kx whose graph is parallel to the straight line 3x − y + 10 = 0.

Let us express from the formula describing the function 3x – y + 10 = 0, the variable y through the variable x. Move the terms 3x and 10 from the left side of the equation to the right side with opposite signs, since when transferring terms from one side of the equation to another, the signs of the transferred terms are reversed.

-y = -3x – 10 – perform term-by-term multiplication of the equation by (-1);

y = 3x + 10.

Graphs of linear functions are parallel in the case when in the equations defining these functions the coefficients in front of x will be equal.

This means that for y = kx the coefficient k must be equal to the coefficient in front of x in the equation y = 3x + 10, i.e. 3. The equation will be y = 3x.

Answer. k = 3; y = 3x.

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