Prove that x²+(1-k)x+k-3=0are real for all real values of k​

First you get "y" by itself. To do so you divide 2 on both sides.

y = 3/2x + 5

To write an equation of a line that is PARALLEL to this equation, the slopes have to be the SAME. So the slope is 3/2.

You then use the equation:

y = mx + b

SInce you know "m" you plug it in.

y = 3/2x + b

Now you need to find b. To do so you plug in the point (2, -5) into this equation.

-5 = 3/2(2) + b

-5 = 3 + b

-8 = b

Finally you plug in b and you get your new equation.

y = 3/2x - 8