Step-by-step explanation:
The pointl-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
We have
[tex]m=\dfrac{1}{3},\ (-2,\ 1)\to x_1=-2,\ y_1=1[/tex]
Substitute:
[tex]y-1=\dfrac{1}{3}(x-(-2))[/tex]
[tex]y-1=\dfrac{1}{3}(x+2)[/tex] → the point-slope form
Convert to the slope-intercept form:
[tex]y-1=\dfrac{1}{3}(x+2)[/tex] use the distributive property
[tex]y-1=\dfrac{1}{3}x+\dfrac{2}{3}[/tex] add 1 = 3/3 to both sides
[tex]y=\dfrac{1}{3}x+\dfrac{5}{3}[/tex] → the slope-intercept form
Convert to the standard form:
[tex]y=\dfrac{1}{3}x+\dfrac{5}{3}[/tex] multiply both sides by 3
[tex]3y=x+5[/tex] subtract x from both sides
[tex]-x+3y=5[/tex] change the signs
[tex]x-3y=-5[/tex] → the standard form
Convert to the general form:
[tex]x-3y=-5[/tex] add 5 to both sides
[tex]x-3y+5=0[/tex] → the general form
