Question

Writing the equation of the line through two given points(-1,5) (3,-1). y=mx+b form

Answer 1

Hello!

First, let's discover the slope using the formula below:

`\text{slope}=(y_2-y_1)/(x_2-x_1)`

Let's use (x1, y1) as (-1, 5) and (x2, y2) as (3, -1). Replacing it in the formula:

`\text{slope}=\frac{-1_{}-(5)_{}}{3_{}-(-1)_{}}=(-1-5)/(3+1)=(-6)/(4)=-(3)/(2)`

So, we know one part of the equation, that m = -3/2.

Now, we have to calculate b:

To do it, let's use the point (x2, y2) = (3, -1) again:

`\begin{gathered} y=mx+b \\ -1=3\cdot(-(3)/(2))+b \\ -1=-(9)/(2)+b \\ -b=-(9)/(2)+1 \\ -b=-(7)/(2) \\ b=(7)/(2) \end{gathered}`

So, we also know that b = 7/2.

Now, writing it as an equation:

`\begin{gathered} y=mx+b \\ y=-(3)/(2)x+(7)/(2) \end{gathered}`