Respuesta :
Answer:
The linear function in slope intercept form of linear equation is;
[tex]y=-\frac{x}{6}-7[/tex]Explanation:
Given that a linear function passes through the points;
[tex]\begin{gathered} (-12,-5) \\ \text{and} \\ (6,-8) \end{gathered}[/tex]To derive its equation, let us apply the point slope form of linear equation;
[tex]y-y_1=m(x-x_1)[/tex]But, firstly let us calculate the slope m of the line;
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]substituting the given points;
[tex]\begin{gathered} m=\frac{-8-(-5)}{6-(-12)}=\frac{-8+5}{6+12} \\ m=\frac{-3}{18} \\ m=-\frac{1}{6} \end{gathered}[/tex]Now let us substitute the slope and the first point into the point slope equation;
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-(-5)=-\frac{1}{6}(x-(-12)) \\ y+5=-\frac{1}{6}x-\frac{1}{6}(12) \\ y+5=-\frac{x}{6}-2 \\ y=-\frac{x}{6}-2-5 \\ y=-\frac{x}{6}-7 \end{gathered}[/tex]Therefore, the linear function in slope intercept form of linear equation is;
[tex]y=-\frac{x}{6}-7[/tex]
