Question

what is the equation of the line in point slope form? (1, -5.5) \\(\circ y = -2x - 5\\) \\(\circ y - 5.5 = -\frac{1}{2}(x - 1)\\) \\(\circ y + 5.5 = -\frac{1}{2}(x - 1)\\) \\(\circ y = -\frac{1}{2}x - 5\\)

Explanation:

Step1: Recall point-slope formula

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

Step2: Identify given point

The line passes through $(1, -6.5)$, so $x_1=1$, $y_1=-6.5$.

Step3: Calculate the slope

Pick a second point on the line, e.g., $(-1, -5.5)$. Use slope formula:
$$m=\frac{y_2-y_1}{x_2-x_1}=\frac{-5.5 - (-6.5)}{-1 - 1}=\frac{1}{-2}=-\frac{1}{2}$$

Step4: Substitute into point-slope form

Substitute $x_1=1$, $y_1=-6.5$, $m=-\frac{1}{2}$ into the formula:
$$y - (-6.5) = -\frac{1}{2}(x - 1)$$
Simplify the left side:
$$y + 6.5 = -\frac{1}{2}(x - 1)$$

Answer:

C. $y+6.5 = -\frac{1}{2}(x-1)$