Q.From the curve $y=x$, draw

Step 1 (i) $y=-x$. Reflection of $y=x$ about the $x$-axis (equivalently about the $y$-axis, since both give the same line here) -- slope flips from $1$ to $-1$.

Step 2 (ii) $y=2x$. Vertical dilation of $y=x$ by factor 2 -- steeper line through the origin, slope $2$.

Step 3 (iii) $y=x+1$. Vertical shift of $y=x$ up by 1 -- parallel line through $(0,1)$ instead of the origin.

Step 4 (iv) $y=\tfrac12x+1$. Vertical dilation by factor $\tfrac12$ (compress toward the $x$-axis, giving slope $\tfrac12$), then shift up by 1 -- line through $(0,1)$ with a gentler slope. …

Rewrite each rule in slope-intercept form and read off the reflection/dilation/translation directl …

• Leaving (v) in the form $2x+y+3=0$ without first solving for $y$, making the slope and intercept (and hence …