### Instruction: Line $l$ has equation $y = 4x - 7$, and line $m$ with equation $y = ax + b$ is perpendicular to line $l$ at $(2,1)$. What is the $y$-coordinate of the point on $m$ that has $x$-coordinate 6?### Response: I know that perpendicular lines have opposite reciprocal slopes, so if the slope of line $l$ is 4, then the slope of line $m$ must be $-1/4$.
That means $a = -1/4$, so the equation of line $m$ is $y = -x/4 + b$.
To find $b$, I can plug in the coordinates of the point where $m$ and $l$ intersect, which is $(2,1)$.
So $1 = -2/4 + b$, or $b = 3/2$.
Now the equation of line $m$ is $y = -x/4 + 3/2$.
To find the $y$-coordinate of the point on $m$ that has $x$-coordinate 6, I can plug in $x = 6$ into the equation of $m$.
So $y = -6/4 + 3/2$, or $y = -3/2 + 3/2$, or $y = 0$.