Step 1
Given;
[tex]\begin{gathered} \text{The equation of the line contains the points;} \\ (-2,14)\text{ and(4,-1)} \end{gathered}[/tex]Required; To find the equation of the line
Step 2
State the equation of a line in slope-intercept form
[tex]\begin{gathered} y=mx+b_{} \\ \text{where, } \\ m=\text{slope} \\ b=\text{ y-intercept} \end{gathered}[/tex]The slope of a line is given as;
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ y_2=-1 \\ y_1=14 \\ x_2=4 \\ x_1=-2 \end{gathered}[/tex][tex]m=\frac{-1-14}{4-(-2)}=\frac{-15}{4+2}=-\frac{15}{6}=-\frac{5}{2}[/tex]Step 3
Find the required equation
[tex]\begin{gathered} \text{The equation of the line becomes;} \\ y=-\frac{5}{2}x+b \\ y=14 \\ x=-2 \\ 14=-\frac{5}{2}(-2)+b \\ 14=5+b \\ b=\text{ 14-5} \\ b=9 \end{gathered}[/tex]Hence, the equation will be written as;
[tex]y=-\frac{5}{2}x+9[/tex]