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.

yes

step-by-step explanation: