The problem has two parts. (c) Find the equation of a line with an undefined slope that contains the point $(-3, 2)$. (d) Given the equation of a line $y - 5 = m(x + 8)$ with slope $m$, identify a point that must be on the line.

1. Problem Description

The problem has two parts.

(c) Find the equation of a line with an undefined slope that contains the point $(-3, 2)$.

(d) Given the equation of a line $y - 5 = m(x + 8)$ with slope $m$, identify a point that must be on the line.

2. Solution Steps

(c) A line with an undefined slope is a vertical line. The equation of a vertical line is of the form $x = c$, where $c$ is a constant. Since the line contains the point $(-3, 2)$, the $x$-coordinate of the point must satisfy the equation of the line. Thus, the equation of the line is $x = -3$.

(d) The given equation is in point-slope form:

$y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is a point on the line and $m$ is the slope.

The equation can be rewritten as $y - 5 = m(x - (-8))$.

Comparing this with the point-slope form, we have $x_1 = -8$ and $y_1 = 5$.

Therefore, the point $(-8, 5)$ must be on the line.

3. Final Answer

(c) $x = -3$

(d) $(-8, 5)$