Question

What is the equation of the blue line?

Answer 1

Answer:

• 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)

${ \rm{slope = \frac{y _{2} - y _{1} }{x _{2} - x _{1} } }} \\ \\ { \rm{m = \frac{3 - 4}{2 - 4} = \frac{ - 1}{ - 2} }} \\ \\ { \underline{ \rm{ \: \: m = \frac{1}{2} \: \: }}}$

→ find the y-intercept:

${ \rm{y = mx + b}} \\ { \rm{3 = ( \frac{1}{2} \times 2) + b}} \\ \\ { \rm{3 = 1 + b}} \\ \\ { \underline{ \rm{ \: \: b = 2 \: \: }}}$

• Therefore, equation of a blue line is

${ \boxed{ \rm{y = \frac{1}{2}x + 2 }}}$