Answer:
[tex] \large \boxed{y = - \frac{1}{9} x - \frac{5}{9} }[/tex]
Step-by-step explanation:
In order to find an equation of a line with two given ordered pairs. We have to find a slope first which we can do by using the formula below.
[tex] \large \boxed{m = \frac{y_2 - y_1}{x_2 - x_1} }[/tex]
m-term is defined as slope in y = mx+b form which is slope-intercept form.
Now we substitute these ordered pairs (x, y) in the formula.
[tex] \large{m = \frac{1 - ( - 2)}{ -14 - 13} } \\ \large{m = \frac{1 + 2}{ - 27} } \\ \large{m = \frac{3}{ - 27} = - \frac{1}{9} }[/tex]
After we calculate for slope, we substitute m-value in slope-intercept form. The slope-intercept form is
[tex] \large \boxed{y = mx + b}[/tex]
We already know m-value as we substitute it.
[tex] \large{y = - \frac{1}{9} x + b}[/tex]
We are not done yet because we need to find the b-term which is our y-intercept. (Note that m-term is slope while b-term is y-intercept)
We can find the y-intercept by substituting either (-14,1) or (13,-2) in the equation. I will be using (13,-2) to substitute in the equation.
[tex] \large{y = - \frac{1}{9} x + b} \\ \large{ - 2 = - \frac{1}{9} (13) + b} \\ \large{ - 2 = - \frac{13}{9} + b} \\ \large{ - 2 + \frac{13}{9} = b} \\ \large{ - \frac{5}{9} = b}[/tex]
Finally, we know b-value. Then we substitute it in our equation.
[tex] \large{y = - \frac{1}{9} x + b} \\ \large{y = - \frac{1}{9} x - \frac{5}{9} }[/tex]
