Answer:
[tex] \displaystyle y = - \frac{1}{2} x - 3[/tex]
Step-by-step explanation:
we are given a line
we want to figure out the equation of theline remember the slope-intercept form of linear equation:
[tex] \displaystyle y = mx + b[/tex]
where:
- m is the slope of the equation
- b is y-intercept
from the graph we can clearly see that the line passes y-intercept at (0,-3) point therefore b is -3
to figure out m we can consider the following formula:
[tex] \displaystyle m = \frac{ y_{2} - y_{1}}{ x_{2} - x_{1}} [/tex]
from the graph we obtain:(0,-3),(2,-4)
[tex] \displaystyle m = \frac{ - 4 - ( - 3)}{ 2 - 0} [/tex]
simplify substraction:
[tex] \displaystyle m = - \frac{ 1}{ 2 } [/tex]
now altogether substitute:
[tex] \displaystyle y = - \frac{1}{2} x - 3[/tex]
and we are done!
