### Home > APCALC > Chapter 3 > Lesson 3.4.1 > Problem3-152

3-152.

Write an equation for $z^\prime$ if $z(x) = 3x^2 + 5x + 1$. Then, write the equation of the tangent line in point slope form at $x = -2$.

The Equation of a Line

When given the slope of a line and one point on the line, we can write the equation of the line in graphing form. This is the translation of the origin of the line $y = mx$ to the point $\left(h, k\right)$. The equation is of the form:

$y=m\left(x-h\right)+k$

Sometimes, you will see the equation of a line also written in point-slope form as $y – k = m\left(x – h \right)$.

To find $h$ and $k$ (the point): $h$ is given as $x = −2$, therefore $k$ is $z(−2)$.

To find $m$ (the slope):evaluate $z^\prime(x)$ at $x = −2$.