Respuesta :
Explanation.
The question asked us to write the equation of the line that passes through the points (2,8) and (-2,10)
To do this, we can use the formula:
[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{y-y_1}{x-x_1}[/tex]In our case, we have
[tex]\begin{gathered} x_1=2 \\ y_1=8 \\ x_2=-2 \\ y_2=10 \end{gathered}[/tex]We will simply put all the values above into the formula to get the equation of the line
[tex]\frac{10-8}{-2-2}=\frac{y-8}{x-2}[/tex]Simplifying further
[tex]\begin{gathered} \frac{2}{-4}=\frac{y-8}{x-2} \\ \\ -\frac{1}{2}=\frac{y-8}{x-2} \end{gathered}[/tex]Cross multiplying
[tex]\begin{gathered} y-8=-\frac{1}{2}\left(x-2\right) \\ y-8=-\frac{1}{2}x+1 \\ y=-\frac{1}{2}x+1+8 \\ y=-\frac{1}{2}x+9 \end{gathered}[/tex]Therefore, the equation of the line is
[tex]y=-\frac{1}{2}x+9[/tex]