The slope-intercept form:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
We have the slope
[tex]m=\dfrac{1}{2}\to y=\dfrac{1}{2}x+b[/tex]
Put the coordinates of the point (6, -3) to the equation of the line:
[tex]-3=\dfrac{1}{2}(6)+b\\\\-3=3+b\qquad\text{subtract 3 from both sides}\\\\-6=b\to b=-6[/tex]
Answer: [tex]y=\dfrac{1}{2}x-6[/tex]
