Respuesta :

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]

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