Given:
A line passes through the point (-6,2) and has a slope of [tex]-\dfrac{3}{2}[/tex].
To find:
The equation of line.
Solution:
If a line passes though a point [tex](x_1,y_1)[/tex] and has a slope m, then the equation of line is
[tex]y-y_1=m(x-x_1)[/tex]
The line passes through the point (-6,2) and has a slope of [tex]-\dfrac{3}{2}[/tex]. So, the equation of line is
[tex]y-2=-\dfrac{3}{2}(x-(-6))[/tex]
[tex]y-2=-\dfrac{3}{2}(x+6)[/tex]
[tex]y-2=-\dfrac{3}{2}(x)-\dfrac{3}{2}(6)[/tex]
[tex]y-2=-\dfrac{3}{2}(x)-9[/tex]
Add 2 on both sides.
[tex]y=-\dfrac{3}{2}(x)-9+2[/tex]
[tex]y=-\dfrac{3}{2}x-7[/tex]
Therefore, the equation of line is [tex]y=-\dfrac{3}{2}x-7[/tex].
