Question

Write an equation in slope-intercept form for the following line:
(-14.1) and (13,-2)

Answer 1

`y=-(1)/(9)x-(5)/(9)`

Explanation:

`(-14,1)(13,-2)`

Use the slope-intercept formula:

`y=mx+b`

m is the slope and b is the y-intercept. Use the slope formula first:

`(y_(2)-y_(1))/(x_(2)-x_(1)) =(rise)/(run)`

Rise over run is the change in the y-axis over the change in the x-axis. Plug in the coordinates:

`(-14(x_(1)),1(y_(1)))\\(13(x_(2)),-2(y_(2)))`

`(-2-1)/(13-(-14))`

Simplify parentheses (two negatives makes a positive):

`(-2-1)/(13+14)`

Simplify:

`(-3)/(27) =-(3)/(27)=-(1)/(9)`

The slope is
`-(1)/(9)`. Insert into the equation:

`y=-(1)/(9)x +b`

Now, to find the y-intercept, take one of the points and substitute for the x and y values of the equation:

`(13,-2)\\-2=-(1)/(9) (13)+b`

Solve for b, the y-intercept. Simplify parentheses:

`-(1)/(9)*(13)/(1)=-(13)/(9)`

`-2=-(13)/(9) +b`

Add
`-(13)/(9)` to both sides:

`-2+(13)/(9)=-(13)/(9) +(13)/(9) +b\\\\-2+(13)/(9) =b`

Simplify:

`-(2)/(1) +(13)/(9)\\\\-(18)/(9)+(13)/(9)\\ \\b=-(5)/(9)`

The y-intercept is
`-(5)/(9)` . Insert this into the equation:

`y=-(1)/(9) x-(5)/(9)`

Finito.