Pls omg - what is the slope of a line perpendicular to the line that passes through (0,2) (4,5)?

So you can solve this using the equation (y2 - y1)/(x2 - x1). This basically means the difference of the y-values (rise) divided (over) the difference of the x-values (run). So basically, this equation is used to find the “rise over run.” In this case, I’ll choose the coordinate pair (0,2) to be my first values, and (4,5) to be my second. Doing it vice versa wouldn’t affect the outcome since both the numerator and denominator would come out to be negative, and a negative divided by a negative is a positive. To solve this, plug in the values to get (5 - 2)/(4 - 0). This reduces to 3/4. To find the slope of the perpendicular line, you would do the opposite reciprocal of that. This means that you would flip the numerator and denominator and change the positive/negative sign to the opposite one of what it is. So the final answer will be -4/3. Hope this helps! Don’t mind my lengthy answers!