Question

Determine m such that the line through points (2m,4) and (m-3,6) has a slope of -5.

Answer 1

We have to use the formula of the slope

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

Where,

`x_1=2m,x_2=m-3,y_1=4,y_2=6,m=-5`

Replacing all these values, we have

`-5=(6-4)/(m-3-2m)`

Now, we solve for m

`\begin{gathered} -5=(2)/(-m-3) \\ -m-3=(2)/(-5) \\ -m=-(2)/(5)+3 \\ m=(2)/(5)-3=(2-15)/(5)=(-13)/(5) \end{gathered}`

Therefore, m must be equal to -13/5 in order to meet the given characteristics.