Answer: 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.
