Answer:
Explanation:
An equation for a line in slope-intercept form is given by
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept.
Now, we are given that slope m = -3; therefore, we have
[tex]y=-3x+b[/tex]Now we only need to find the y-intercept b.
Luckily, we know that the line passes through the point (6, -3), meaning the above equation must satisfy x = 6, y = -3.
Putting in x = 6 and y= -3 in the above equation gives
[tex]-3=-3(6)+b[/tex][tex]-3=-18+b[/tex]Adding 18 to both sides of the equation gives
[tex]-3+18=-18+b+18[/tex][tex]-3+18=b[/tex][tex]15=b[/tex]Hence, the value of b is 15, and therefore, the equation of the line is
[tex]\boxed{y=-3x+15}[/tex]