Question

find an equation of the line containing the given pair of points.\\((-1, -9)\\) and \\((-3, -8)\\)\
the equation of the line in slope - intercept form is \\(y =\square\\).\
(simplify your answer. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Calculate the slope

Let $(x_1,y_1)=(-1,-9)$ and $(x_2,y_2)=(-3,-8)$.
Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{-8-(-9)}{-3-(-1)}=\frac{1}{-2}=-\frac{1}{2}$

Step2: Find y-intercept $b$

Use $y=mx+b$, substitute $m=-\frac{1}{2}$ and $(x_1,y_1)=(-1,-9)$:
$-9 = -\frac{1}{2}(-1) + b$
$-9 = \frac{1}{2} + b$
$b = -9 - \frac{1}{2} = -\frac{19}{2}$

Step3: Write slope-intercept equation

Substitute $m=-\frac{1}{2}$ and $b=-\frac{19}{2}$ into $y=mx+b$.

Answer:

$y = -\frac{1}{2}x - \frac{19}{2}$