Given:
The points of the line are,
[tex]\begin{gathered} (x_1,y_1)=(-3,-2) \\ (x_2,y_2)=(1,5) \end{gathered}[/tex]
The objective is to find the equation of the line in terms of x.
Explanation:
The general equation of a straight line using two points is,
[tex]\frac{y-y_1}{y_2-y_1}=\frac{x-x_1}{x_2-x_1}\text{ . . . .(1)}[/tex]
On plugging the given values in equation (1),
[tex]\frac{y-(-2)}{5-(-2)}=\frac{x-(-3)}{1-(-3)}[/tex]
On further solving the above equation,
[tex]\begin{gathered} \frac{y+2}{5+2}=\frac{x+3}{1+3} \\ \frac{y+2}{7}=\frac{x+3}{4} \\ 4(y+2)=7(x+3) \\ 4y+8=7x+21 \\ 4y=7x+21-8 \\ 4y=7x+13 \\ y=\frac{7}{4}x+\frac{13}{4} \end{gathered}[/tex]
Hence, the equation of the line in terms of x is y = (7x/4)+(13/4).
