What is the equation of a line that goes through the point (0,-3) and is perpendicular to the line y=-2/5x+6

Answer 1

The line has a slope of -2/5.

The perpendicular slope will be the opposite reciprocal of the original slope. In this case, 5/2.

So, the equation would be y = 5/2x plus or minus the y-intercept which you must calculate from the point (0,-3)

That point is the y intercept since x is 0. Therefore, the equation is y = 5/2x - 3. I suggest you draw them on graph paper to see this, or use an online graphing tool like https://www.desmos.com/calculator