Question

6 write the slope intercept form of the equation of the line.
equation:

Explanation:

Step1: Recall slope-intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Find the y - intercept ($b$)

The y - intercept is the point where the line crosses the y - axis. From the graph, the line crosses the y - axis at $(0,-1)$. So, $b=-1$.

Step3: Calculate the slope ($m$)

We can use two points on the line to calculate the slope. Let's use the points $(-2,0)$ and $(0, - 1)$. The formula for slope $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(-2,0)$ and $(x_2,y_2)=(0,-1)$. Then $m=\frac{-1 - 0}{0-(-2)}=\frac{-1}{2}=-\frac{1}{2}$.

Step4: Write the equation

Substitute $m = -\frac{1}{2}$ and $b=-1$ into the slope - intercept form $y=mx + b$. We get $y=-\frac{1}{2}x-1$.

Answer:

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