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Sagot :
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]
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