Question

What is the equation of the blue line?

Answer 1

• From the general equation of a line:

`{ \rm{y = mx + b}} \\`

• m is slope
• b is y-intercept.

→ Consider points (4, 4) and (2, 3)

`{ \rm{slope = (y _(2) - y _(1) )/(x _(2) - x _(1) ) }} \\ \\ { \rm{m = (3 - 4)/(2 - 4) = ( - 1)/( - 2) }} \\ \\ { \underline{ \rm{ \: \: m = (1)/(2) \: \: }}}`

→ find the y-intercept:

`{ \rm{y = mx + b}} \\ { \rm{3 = ( (1)/(2) * 2) + b}} \\ \\ { \rm{3 = 1 + b}} \\ \\ { \underline{ \rm{ \: \: b = 2 \: \: }}}`

• Therefore, equation of a blue line is

`{ \boxed{ \rm{y = (1)/(2)x + 2 }}} \\`