Question

(0'-10)(-10,2) what is the linear equation

Answer 1

We are asked to find the linear equation of a line that passes through the points (0,-10) and (-10,2). To do that, let's remember the general form of a line equation:

`y=mx+b`

Where "m" is the slope of the line and "b" the y-intercept. To determine the slope we use the following formula:

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

In our case we have:

`\begin{gathered} (x_1,y_1)=(0,-10) \\ (x_2,y_2)=(-10,2) \end{gathered}`

Replacing in the equation for the slope:

`m=(2-(-10))/(-10-0)`

Solving the operations:

`m=(2+10)/(-10)=(12)/(-10)=-(6)/(5)`

We replace the value of the slope in the general equation for the line:

`y=-(6)/(5)x+b`

Now we need to replace one of the given points in order to find the y-intercept "b". We will use the point (x,y) = (0,-10). This means that when x = 0, y = -10:

`-10=-(6)/(5)(0)+b`

Solving the operations we get:

`-10=b`

We replace the value of "b" in the general equation for the line:

`y=-(6)/(5)x-10`

And thus we find the linear equation.