find the equation of the new graph

[bumblebee123]

can anyone teach me how to answer this question? I've never come across one like this before

question: the graph y = 3x - 2 is reflected in the line with equation y = x. Find the equation of the new graph

any help would be really appreciated!

 

[pka]

can anyone teach me how to answer this question? I've never come across one like this before:question: the graph y = 3x - 2 is reflected in the line with equation y = x. Find the equation of the new graph.

This is a standard problem in transforms of the plane. The point \(\displaystyle (p,q)\) is reflected in the line \(\displaystyle y=x\) is \(\displaystyle (p,q)\to(q,p)\)
\(\displaystyle \begin{align*}y&=3x-2 \\x&=3y-2\\3y&=x+2\\x-3y+2&=0 \end{align*}\)
Please SEE HERE Note that the point \(\displaystyle (1,1)\)\(\displaystyle is on all three lines.\)

 

[bumblebee123]

ah, so i need to replace y with x ( obviously because y=x )

 

[Harry_the_cat]

When you reflect any point in the line y=x, the x and y coordinates of the point are swapped.

Draw a diagram and see for yourself. Draw a set of axes and draw in the line y=x (45 degrees through the origin). Now pick a few points anywhere in the plane and reflect them in the line y=x. You'll see that the co-ordinates swap.

(It's not really for the reason you gave in brackets. For example, if you were reflecting in the line y=2x you don't just replace y with 2x.)