Question

What is the slope of the line passing through the following points: #(-7,11), (9, -10) #?

Answer 1

`"slope "=-21/16`

Explanation:

`"to calculate the slope m use the "color(blue)"gradient formula"`

`•color(white)(x)m=(y_2-y_1)/(x_2-x_1)`

`"let "(x_1,y_1)=(-7,11)" and "(x_2,y_2)=(9,-10)`

`rArrm=(-10-11)/(9-(-7))=(-21)/16=-21/16`

Answer 2

`y=-21/16x+29/16`

Explanation:

First we find `m` which is slope. Slope formula is
`m=(y_2-y_1)/(x_2-x_1)`

Where
`y_2=-10`
`y_1=11`
`x_2=9`
`x_1=-7`

Now we just plug it in, giving us
`m=(-10-11)/(9-(-7))`

`m=(-21)/(9+7)`

`m=(-21)/16`

Now that we have `m` we can use the line formula to finish the problem.
The line formula is
`y-y_1=m(x-x_1)`

`y-11=(-21/16)(x-(-7))`

`y-11=-21/16(x+7)`

`y-11=-21/16x+(-21(7))/16`

`y-11=-21/16x-147/16`

Now we add `11` to both sides giving us
`y=-21/16x-147/16+11`

Now we find a common denominator between the constants `11/1` and `-147/16`

`y=-21/16x+(11(16))/(1(16))-147/16`

`y=-21/16x+176/16-147/16`

`y=-21/16x+(176-147)/16`

`y=-21/16x+29/16`