Question

Assuming that the graph of y = x^2 - 5x has been drawn, find the equation of the line which you should draw to solve the equation: x^2 - 5x = 3?

Answer 1

see below

Explanation:

graph drawn

`color(blue)(y)=color(red)(x^2-5x)`

equation to solve

`color(red)(x^2-5x)=color(blue)(3)`

a comparison of the two eqns shows that

`y=3` and that is the graph to be drawn.

If such a comparison is not straightforward , the way to find the eqn is to subtract both eqns given

so in this case

`y=x^2-5x`
`" "-`

`3=x^2-5x`

subtracting

`y-3=0+0`

`y-3=0=>y=3`

the solution(s) to the equation is/are then found where the graphs intersect.