Question

Write the equation of the line in fully simplified slope-intercept form.

Answer 1

Explanation:

Choose two points on the graph: (-6,-7) and (6,-9)

The straight line equation is: y=mx+b

`\displaystyle\\\boxed {The\ slope\ m=(y_2-y_1)/(x_2-x_1) }\\\\x_1=-6\ \ \ \ x_2=6\ \ \ \ \ y_1=-7\ \ \ \ y_2=-9\\\\m=(-9-(-7))/(6-(-6)) \\\\m=(-9+7)/(6+6) \\\\m=(-2)/(12) \\\\m=-(1)/(6)\\\\Hence,\ y=-(1)/(6)x+b\ \ \ \ \ (1)`

To determine the coefficient b, take any of the two points,

for example (-6,-7), that is, x=-6 y=-7

Substitute these values into formula (1):

`\displaystyle\\-7=-(1)/(6)(-6) +b\\\\-7=1+b\\\\-7-1=1+b-1\\\\-8=b\\\\Thus,\ b=-8\\\\The\ result\ is\ y=-(1)/(6)x-8`