Equations of Tangent Lines Worksheets

How to solve it: a worked example

Write the equation of the tangent line at the given x-value, in slope-intercept form.

1. Startf(x) = −3x² − 4x − 8, x = 2
2. The pointf(2) = −28
3. The slopef′(x) = −6x − 4, f′(2) = −16
4. Point-slope form, then solve for yy − (−28) = −16(x − 2)
5. Theny = −16x + 4
6. Answery = −16x + 4

Common mistakes to watch for

• Using f(a) as the slope instead of f′(a).
• Substituting a into f′ but using the general derivative as the slope.
• Sign errors when moving to slope-intercept form.

Tip: tick “Step-by-step answer key” in the generator to print each step for marking.