Question

PLEASE HELP! I will give the brainliest to most helpful and correct answer! Find the equation of the line.

Answer 1

Y = -1/4x - 6
Your y intercept is -6 or where your line crosses the y axis and your slope is rise over run your rise is -1 and your run is 4 to the right

Answer 2

Answer:

y = $- \frac{1}{4}$x - 3

Step-by-step explanation:

1. Slope intercept form

There are many ways to denote the equation of a line, this problem requires the equation to be denoted in slope-intercept form.

The following equation is the general formula for slop-intercept form;

y = mx + b

were "m" is the slope, and "b" is the y-intercept.

In order to solve this problem, one needs the slope and the y-intercept.

2. Finding the slope

The slope of a line is the line's rate of change, and is often called; $\frac{rise}{run}$. The general formula for finding the slope of a line is the following;

$\frac{y_{2} -y_{1}}{x_{2} - x_{1}}$

To solve for the slope, one has to pick two points on the line to input as $y_{2}, y_{1}, x_{2}, x_{1}$, I choose the following points;

(-4, -5), (0, -6)

Substitute in the values;

$x_{1} = -4\\y_{1} = -5\\\\x_{2} = 0\\y_{2} = -6$

$\frac{(-6) -(-5)}{0 -(-4)}$

Simplify;

$\frac{-6+5}{0+4} \\\\\frac{-1}{4}\\\\- \frac{1}{4}$

3. Finding the y-intercept

The y-intercept is the place where the line intersects the y-axis. In essence, if one uses this line to find where x equals zero, what does y equal. In this case, this point is given on the graph, it is;

(0, -3)

In the "b" value of the slope-intercept form of a line, one only uses the value in the y-position of the ordered pair, in the equation. This is because the x-value has no value, it is always zero when is working with the y-intercept.

4. Putting it together

Now that one has found the slope, and y-intercept, one now just has to put it into the general formula to get the complete equation of a line.

y = mx + b

m = $- \frac{1}{4}$

b = -3

y = $- \frac{1}{4}$x - 3