Question

What’s the equation for points (2,13) and (4,6)

Answer 1

The points we have are:

(2,13) and (4,6)

I will label this points as follows:

`\begin{gathered} x_1=2 \\ y_1=13 \\ x_2=4 \\ y_2=6 \end{gathered}`

To find the equation for this line, first we need to find the slope between the points with following slope formula:

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

Where m is the slope.

Substituting our known values:

`\begin{gathered} m=(6-13)/(4-2) \\ m=(-7)/(2) \end{gathered}`

Next, we need to use the point-slope equation:

`y=m(x-x_1)+y_1`

And substitute our values, including the slope:

`y=-(7)/(2)(x-2)+13`

Using the distributive property to multiply -7/2 by x and by -2:

`\begin{gathered} y=-(7)/(2)x+7+13 \\ y=-(7)/(2)x+20 \end{gathered}`

Answer:

`y=-(7)/(2)x+20`