Question

What is the equation of this graphed line?

Enter your answer in slope-intercept form in the box.

Answer 1

`y=-(1)/(3)x-5`

Explanation:

Given:

The two points on the line are:

`(x_1,y_1)=(-6,-3)\\(x_2,y_2)=(6,-7)`

Now, for a line with two points on it, the slope of the line is given as:

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

For the points
`(x_1,y_1)=(-6,-3)\ and\ (x_2,y_2)=(6,-7)`, slope is:

`m=(-7-(-3))/(6-(-6))\\m=(-7+3)/(6+6)\\m=(-4)/(12)=-(1)/(3)`

Now, for a line with slope 'm' and a point
`(x_1,y_1)` on it is given as:

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

Plug in all the values and determine the equation of the line. This gives,

`y-(-3)=-(1)/(3)(x-(-6))\\\\y+3=-(1)/(3)(x+6)\\\\y+3=-(1)/(3)x-(1)/(3)* 6\\\\y+3=-(1)/(3)x-2\\\\y=-(1)/(3)x-2-3\\\\y=-(1)/(3)x-5`

Therefore, the equation of the line is:

`y=-(1)/(3)x-5`