We are required to find the equation of a straight line passing through two given points .
First we can calculate the gradient / slope
[tex]\begin{gathered} x_1=-2 \\ y_1=3 \\ x_2=4 \\ y_2=15 \end{gathered}[/tex]Calculating slope(m) below
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]\begin{gathered} m=\frac{15-3}{4-(-2)} \\ m=\frac{12}{6} \\ m=2 \end{gathered}[/tex]Using the formula y = mx + c at the point any of the two given points .... we can use ( 4 , 15 ) ... we have
[tex]\begin{gathered} y=2x+c \\ x=4,y=15 \\ 15=2(4)+c \\ 15=8+c \\ c=7 \end{gathered}[/tex]The required straight line equation will be obtained using y=mx+c as;
[tex]y=2x+7[/tex]Here is a graph of the line
Hence the equation of the line is y=2x + 7
