Respuesta :

The points we have are:

(2,13) and (4,6)

I will label this points as follows:

[tex]\begin{gathered} x_1=2 \\ y_1=13 \\ x_2=4 \\ y_2=6 \end{gathered}[/tex]

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

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Where m is the slope.

Substituting our known values:

[tex]\begin{gathered} m=\frac{6-13}{4-2} \\ m=\frac{-7}{2} \end{gathered}[/tex]

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

[tex]y=m(x-x_1)+y_1[/tex]

And substitute our values, including the slope:

[tex]y=-\frac{7}{2}(x-2)+13[/tex]

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

[tex]\begin{gathered} y=-\frac{7}{2}x+7+13 \\ y=-\frac{7}{2}x+20 \end{gathered}[/tex]

Answer:

[tex]y=-\frac{7}{2}x+20[/tex]