Question

(a) write the equation in slope-intercept form, and determine the slope and y-intercept.
(b) graph the equation using the slope and y-intercept.
$-x - 4y = 4$
part: 0 / 2
part 1 of 2
the slope is $\square$
the y-intercept is $(\square, \square)$
the equation written in slope-intercept form is $\square$

Explanation:

Step 1: Recall slope - intercept form

The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the $y$ - intercept (the point where the line crosses the $y$ - axis, and its coordinates are $(0,b)$). We need to rewrite the given equation $-x - 4y=4$ in this form.
First, we want to solve the equation for $y$.
Start with the original equation: $-x - 4y = 4$.
Add $x$ to both sides of the equation: $-4y=x + 4$.

Step 2: Solve for y

Divide each term in the equation $-4y=x + 4$ by $-4$ to isolate $y$.
$y=\frac{x}{-4}+\frac{4}{-4}$.
Simplify the fractions: $y=-\frac{1}{4}x - 1$.

Step 3: Identify the slope and y - intercept

Now that the equation is in slope - intercept form $y = mx + b$, we can identify the slope $m$ and the $y$ - intercept $b$.
For the equation $y=-\frac{1}{4}x - 1$, the slope $m = -\frac{1}{4}$ and the $y$ - intercept $b=-1$. The $y$ - intercept as a point is $(0, - 1)$ because when $x = 0$, $y=-1$.

Answer:

The equation written in slope - intercept form is $y=-\frac{1}{4}x - 1$.
The slope is $-\frac{1}{4}$.
The $y$ - intercept is $(0,-1)$.