can someone help with this graphing math question?

Question

The diagram shows the line $2y=x+5$ and the curve $y=x^2-4x+7$, which intersects the points A and B. How do you find the $x$-coordinates and also the equation of the tangent to the curve at B?

Answer 1

$2y=x+5$ implies $y=\frac{x}{2}+\frac{5}{2}$

Let $y=y$, namely $\frac{x}{2}+\frac{5}{2}=x^2-4x+7$

Solve for real $x$, should they exist...

As for the tangent, take the derivative of the curve with respect to $x$, namely $$y'(B)=2(B)-4$$

Evaluate $$\lim_{h->0}\frac{(B+h)^2-4(B+h)+7-B^2+4B-7}{h}$$