Answer:
Part A) The slope is
![m=-(1)/(2)](https://img.qammunity.org/2020/formulas/mathematics/high-school/949vzv7fnr3yt14uoxkzqanql7dj8l30nf.png)
Part B) The equation of the line is
![y=-(1)/(2)x-1](https://img.qammunity.org/2020/formulas/mathematics/college/vzn35q7og7vbeohljs05att9vb3g6st1kx.png)
Explanation:
Part A) What is the slope of the graph?
we know that
The formula to calculate the slope between two points is equal to
![m=(y2-y1)/(x2-x1)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/3alxf865ejd0fdnwnbs21cssprdlquqoeh.png)
Looking at the graph it takes any two points
(-2,0) and (0,-1)
substitute the values in the formula
![m=(-1-0)/(0+2)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/ug6f6yc6ry6pktldo1qalrpfizkjn7ppnc.png)
![m=(-1)/(2)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/4jc1pnbkue9uauxveekcmt5c86opj6ppbz.png)
![m=-(1)/(2)](https://img.qammunity.org/2020/formulas/mathematics/high-school/949vzv7fnr3yt14uoxkzqanql7dj8l30nf.png)
Part B) Write an equation for the line
we know that
The equation of the line in slope intercept form is
![y=mx+b](https://img.qammunity.org/2020/formulas/mathematics/high-school/8nudzfk4b5l0arb9iixag2w8am6zn99zlr.png)
where
m is the slope
b is the y-coordinate of the y-intercept
we have
![m=-(1)/(2)](https://img.qammunity.org/2020/formulas/mathematics/high-school/949vzv7fnr3yt14uoxkzqanql7dj8l30nf.png)
----> the y-intercept is the point (0,-1)
substitute
![y=-(1)/(2)x-1](https://img.qammunity.org/2020/formulas/mathematics/college/vzn35q7og7vbeohljs05att9vb3g6st1kx.png)