I’m not sure why I can’t solve this one, any help is welcome! Please find enclosed screenshot. My thoughts:

We are looking for a perpendicular line so current coefficient is -(1/2)x

then taking the reciprocal means 2 and negating it means it becomes positive just 2

y = 2x + b

Then to figure out b, we fill in the coordinates (1,6)

6 = 2 . 1 + b

6 = 3 + b

b = 6 - 3 = 3

summing 2 + 3 = 5 but the answer is 6…

Equation of the line given :

y = -\dfrac{1}{2}x+5 \\
\text{thus, it's slope =} -\dfrac{1}{2}

Now, to be perpendicular, the product of their slope = -1

-\dfrac{1}{2} \times \text{unknown_slope} = -1 \\
\text{Or, unknown_slope = } 2

Now, unknown_slope = \dfrac{Y_2-Y1}{X_2-X_1}

And because line passes through point (1,6)

\begin{aligned}
\dfrac{Y_2-6}{X_2-1} &= \text{ unknown_slope} \\
\dfrac{(Y_2-6)}{(X_2-1)} &= 2\\
(Y_2-6) &= 2\times(X_2-1)\\
Y_2 &= 2X_2+4
\end{aligned}

we have our equation of line :

Y_2 = 2X_2+4

question asking m + b

thus, subsitution m = 2 and b = 4 we get

m+b =6

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I found your mistake.

6=2.1+b

so, 6=2+b

and b=4

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so helpful, thank u! my brain sometimes just stops working