Question

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

Answer 1

Answer

$y=6x+9$

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:

$y=6x+9$