Respuesta :
The line passes through the points (-5, 2) and (10,-1) and we need to find the equation of the line.
Step 1: We will label this coordinates as follows:
[tex]\begin{gathered} x_1=-5 \\ y_1=2 \\ x_2=10_{} \\ y_2=-1 \end{gathered}[/tex]Step 2. We calculate the slope "m" with the slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]substituting our values:
[tex]m=\frac{-1-2}{10-(-5)}[/tex]solving the operations we find that the slope is:
[tex]\begin{gathered} m=\frac{-3}{10+5} \\ m=-\frac{3}{15} \\ m=-\frac{1}{5} \end{gathered}[/tex](Note: in the last line we simplified the fraction 3/15 to 1/5 dividing by 3)
Step 3. We use the the point-slope squation which is:
[tex]y=m(x-x_1)+y_1[/tex]And we substitute all of the known values of the slope m, and the point (x1, y1) which is (-5,2):
[tex]y=-\frac{1}{5}(x-(-5))+2[/tex]Simplifying the expression:
[tex]y=-\frac{1}{5}(x+5)+2[/tex][tex]\begin{gathered} y=-\frac{1}{5}x-\frac{1}{5}(5)+2 \\ y=-\frac{x}{5}-1+2 \end{gathered}[/tex]we add the -1 +2 and get the final result:
[tex]y=-\frac{x}{5}+1[/tex]Answer:
[tex]y=-\frac{x}{5}+1[/tex]