Question

How do you find the value of `k` so that the slope of the line containing the points `(- 3,k) and (2,4) " is " -2`?

Answer 1

`k = 14`

Explanation:

We know the slope of a line has the equation:

`(Delta y )/ (Delta x) = "change in y " / "change in x " = (y_2-y_1)/(x_2-x_1)`

Therefore:

`(4-k)/(2-(-3)) = -2`

`=> (4-k) / 5 = -2`

Multiply by 5:

`=> 4-k = -10`

`=> 4 = -10+k`

`=> 4+10 = k`

`=> color(red)(k = 14`

Answer 2

`k=14`

Explanation:

`"the slope of a line (m) is calculated using the "color(blue)"gradient formula"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(2/2)|)))`

`"let "(x_1,y_1)=(-3,k)" and "(x_2,y_2)=(2,4)`

`rArrm=(4-k)/(2-(-3))=(4-k)/5`

`"now "m=-2`

`rArr(4-k)/5=-2`

`"multiply both sides by 5"`

`cancel(5)xx(4-k)/cancel(5)=(5xx-2)`

`rArr4-k=-10`

`"subtract 4 from both sides"`

`cancel(4)cancel(-4)-k=-10-4`

`rArr-k=-14`

`"multiply through by "-1`

`rArrk=14`

`color(blue)"As a check"`

`(4-14)/5=(-10)/5=-2larr" True"`