Equation of a Line Given Slope and a Point

$y = \red{ m } x + b \\ y = \red{ \frac 1 2 } x + b$

$\red 3 = \frac 1 2 (\red 2)+ b$

$3 = 1 + \red b \\ 3 - 1 = \red b \\ 2 = \red b$

$y = \frac 1 2 x + 2$

$y = \red m x + b \\ y = \red {10} x + b$

$y = \red {10} x + b \\ \red { 34 } = 10 (\red 3) + b \\ $

$34 - 30 = b \\ 4 = b$

$y = 10x + 4$

$y = \red m x + b \\ y = \red 3 x + b$

$y = \red 3 x + b \\ 23 = \red 3 (6) + b$

$23 = \red 3 (6) + b \\ 23 = 18 + \red b \\ 5 = b$

$y = 3x + 5$

$y = \red 0x + b$

$y = \red0 x + b \\ 5 = 0(7) + b$

$b = 5$

$y = 0x + 5 \\ y = 5$