Write an equation that is parallel and perpendicular to the points (-2,-3)

 y=2x+1

Step-by-step explanation:

Find the slope of the existing line by calculating a Rise/Run (the change in y for a change in x).  Pick any two points on the existing line.  I picked (-2,3) and (2,1).

Rise = 1-3 = -2

Run = 2-(-2)= 4

Rise/Run (slope) = -2/4 or -0.5

Although we don't need it, the equation for the existing line is y=-0.5x+b.  B is easy to find, since it is the value of y at x=0 (the y-intercept).  y=2 at x=0, so the existing line's equation is y=-0.5x+2

A line that is perpendicular to this line will have a slope that is the negative inverse of the reference line.  The negative inverse of -0.5 is -1/-0.5 or 2.  The new line will look like this:

y = 2x + b

To find b, use he given point (-2,-3) in the new equation and solve for b:

y = 2x + b

-3 = 2(-2) + b

b = 1

The equation of the line perpendicular to the reference line and going through (-2,-3) is

y = 2x +  1

See attached graph.

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.