Question

Find y if the slope between ( 7 , y ) and ( 9 , − 8 ) is − 3 .

Answer 1

Answer: y = -2

Explanation:

I am going to use our slope formula:

`\bigstar\quad\underline{\boxed{\sf{m=\cfrac{y_2-y_1}{x_2-x_1}}}}`

Put in all the required values :

`\bf{-3=\cfrac{-8-y}{9-7}}`

Simplify:

`\bf{-3=\cfrac{-8-y}{2}}`

Multiply both sides by 2:

`\bf{-6=-8-y}`

Add 8 to both sides

`\bf{-8-y=-6}`

`\bf{-y=-6+8}`

`\bf{-y=2}`

`\bf{y=-2}`

Therefore, the answer is y = -2.

Answer 2

Answer: y = -2

Explanation:

We can use the slope formula to help us solve for y.

Given:

`\displaystyle (y_(2) -y_(1) )/(x_(2) -x_(1) ) =\text{slope}`

Substitute:

`\displaystyle (-8 -y )/(9-7) =-3`

Subtract:

`\displaystyle (-8 -y )/(2) =-3`

Multiply both sides of the equation by 2:

-8 - y = -6

Add 8 to both sides of the equation:

-y = 2

Divide both sides of the equation by -1:

y = -2

We can check our work by graphing and using "rise over run," see attached.