Write the equation of lines shown on the graph.

Step-by-step explanation:

red       y = -3/2 x - 3       m = -3/2    (y2-y1) / (x2 - x1)   b = -3

blue     y = 2x + 3            m = 2   rise/run      b = 3

black     your turn           m  = ?   (0, -1) and (3, 0)  two points on the black line

                                       m = ?   (y2-y1) / (x2 - x1)  =  (0-(-1)) / (3 - 0)  = (0+1)/(3-0)

                                       m = ?

                                       b = the y value when x = 0, which is one of the points

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)

graph b

step-by-step explanation:

one solution- graph a (clear intercepting point.)

no solution- graph b (they're parallel, there will never be a point of interception.)

infinite solutions- graph c (all points intercept.)