Question

A linear function passes through the points (-12, -5) and (6, –8). What is its equation

Answer 1

The linear function in slope intercept form of linear equation is;

`y=-(x)/(6)-7`

Step-by-step explanation:

Given that a linear function passes through the points;

`\begin{gathered} (-12,-5) \\ \text{and} \\ (6,-8) \end{gathered}`

To derive its equation, let us apply the point slope form of linear equation;

`y-y_1=m(x-x_1)`

But, firstly let us calculate the slope m of the line;

`m=(y_2-y_1)/(x_2-x_1)`

substituting the given points;

`\begin{gathered} m=(-8-(-5))/(6-(-12))=(-8+5)/(6+12) \\ m=(-3)/(18) \\ m=-(1)/(6) \end{gathered}`

Now let us substitute the slope and the first point into the point slope equation;

`\begin{gathered} y-y_1=m(x-x_1) \\ y-(-5)=-(1)/(6)(x-(-12)) \\ y+5=-(1)/(6)x-(1)/(6)(12) \\ y+5=-(x)/(6)-2 \\ y=-(x)/(6)-2-5 \\ y=-(x)/(6)-7 \end{gathered}`

Therefore, the linear function in slope intercept form of linear equation is;

`y=-(x)/(6)-7`