Given A(5,3) and O(0,0), find a point B that makes the following true: m(A,B)=3

A point B is (1 , -9)Step-by-step explanation:The formula of the slope of a line is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] where [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] are two points lie on the lineA (5 , 3) and O (0 , 0) are two pointsm(A , B) = 3 ⇒ (the slope of AB = 3)We need to find a point B that makes that trueAssume that point B is (x , y)∵ Point A = (5 , 3)∵ Point B = (x , y)∴ [tex]x_{1}=5[/tex] and [tex]x_{2}=x[/tex] ∴ [tex]y_{1}=3[/tex] and [tex]y_{2}=y[/tex] - Substitute these values in the formula of m∴ [tex]m=\frac{y-3}{x-5}[/tex]∵ m(A , B) = 3- Equate the formula of the slope by 3∴ [tex]\frac{y-3}{x-5}=3[/tex]- By using cross multiplication∴ y - 3 = 3(x - 5)- Simplify the right hand side∴ y - 3 = 3x - 15- Add 3 for both sides∴ y = 3x - 12To find point B chose any value for x and substitute it in theequation to find y∵ x = 1∴ y = 3(1) - 12 = 3 - 12∴ y = 9∴ Point B = (1 , -9)V.I.N: You can find many values of point B by chose different values of x and find the corresponding values of yA point B is (1 , -9)Learn more:You can learn more about the slope of the linear equation in brainly.com/question/4152194#LearnwithBrainly