Question

given the equation $y + 2 = -\frac{21}{22}(x + 16)$, convert the equation to slope intercept form.
$\bigcirc$ $y = -\frac{21}{22}x - \frac{190}{11}$
$\bigcirc$ $y = -\frac{21}{22}x + 14$
$\bigcirc$ $y = -\frac{21}{22}x + 18$
$\bigcirc$ $y = -\frac{21}{22}x + \frac{190}{11}$

Explanation:

Step1: Distribute the slope

We start with the given equation \( y + 2 = -\frac{21}{22}(x + 16) \). First, we distribute the \( -\frac{21}{22} \) to both terms inside the parentheses.

$$ y + 2 = -\frac{21}{22}x - \frac{21}{22} \times 16 $$

Step2: Calculate the constant term

Now, we calculate \( -\frac{21}{22} \times 16 \). Let's do that:

$$ -\frac{21}{22} \times 16 = -\frac{336}{22} = -\frac{168}{11} $$

So the equation becomes:

$$ y + 2 = -\frac{21}{22}x - \frac{168}{11} $$

Step3: Isolate y

Next, we subtract 2 from both sides to isolate y. We need to express 2 as a fraction with a denominator of 11 to combine the constant terms. \( 2 = \frac{22}{11} \).

$$ y = -\frac{21}{22}x - \frac{168}{11} - \frac{22}{11} $$

Step4: Combine the constant terms

Now, we combine the two constant terms:

$$ -\frac{168}{11} - \frac{22}{11} = -\frac{190}{11} $$

So the equation in slope-intercept form (\( y = mx + b \)) is:

$$ y = -\frac{21}{22}x - \frac{190}{11} $$

Answer:

\( y = -\frac{21}{22}x - \frac{190}{11} \) (corresponding to the first option: \( y = -\frac{21}{22}x - \frac{190}{11} \))