Question

Determine the equation of the tangent to y=x^2+6x+9 which has a slope of 6.

Answer 1

`y=6x+9`

Step-by-step explanation

Given

`y=x^2+6x+9`

The slope of the tangent is the 1st derivative, thus we have to calculate it:

`y^(\prime)=2x+6(1)+0`
`y^(\prime)=2x+6`

Then, we have to set the equation to 6 as it is the slope:

`6=2x+6`
`2x=6-6`
`2x=0`
`x=0`

Then, if we calculate the value of y when x = 0 in the given equation:

`y=0^2+6(0)+9`
`y=9`

By using this point and the slope-intercept form of the equation of the line (y = mx+b) we get:

`9=6(0)+b`
`9=b`
`b=9`

Finally, the equation is:

`y=6x+9`