The equation of a line in point-slope form is expressed as:
[tex]y-y_0=m(x_{}-x_0)[/tex]where:
• m is the, slope ,of the line
,• (x0, y0) is, any point ,on the line
Given the following parameters
[tex]\begin{gathered} m=-\frac{3}{2} \\ (x_0,y_0)=(-3,-2) \end{gathered}[/tex]Substitute the given parameters into the formula to have:
[tex]\begin{gathered} y-(-2)=-\frac{3}{2}(x_{}-(-3)) \\ y+2=-\frac{3}{2}(x+3) \\ 2(y+2)=-3(x_{}+3) \end{gathered}[/tex]Expand and write in slope-intercept form y = mx + b
[tex]\begin{gathered} 2y+4=-3x-9 \\ 2y=-3x-9-4 \\ 2y=-3x-13 \\ y=-\frac{3}{2}x-\frac{13}{2} \end{gathered}[/tex]Hence the equation of the line in slope-intercept form is expressed as
y = -3/2x - 13/2