Question

What is the equation of the line that passes through the point (6,-3) and has aslope of – 3?

Answer 1

Explanation:

An equation for a line in slope-intercept form is given by

`y=mx+b`

where m is the slope and b is the y-intercept.

Now, we are given that slope m = -3; therefore, we have

`y=-3x+b`

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

`-3=-3(6)+b`
`-3=-18+b`

Adding 18 to both sides of the equation gives

`-3+18=-18+b+18`
`-3+18=b`
`15=b`

Hence, the value of b is 15, and therefore, the equation of the line is

`\boxed{y=-3x+15}`