Question

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

Answer 1

A point B is (1 , -9)

Step-by-step explanation:

The formula of the slope of a line is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

where $(x_{1},y_{1})$ and $(x_{2},y_{2})$ are two points

lie on the line

• A (5 , 3) and O (0 , 0) are two points
• m(A , B) = 3 ⇒ (the slope of AB = 3)

We need to find a point B that makes that true

Assume that point B is (x , y)

∵ Point A = (5 , 3)

∵ Point B = (x , y)

∴ $x_{1}=5$ and $x_{2}=x$

∴ $y_{1}=3$ and $y_{2}=y$

- Substitute these values in the formula of m

∴ $m=\frac{y-3}{x-5}$

∵ m(A , B) = 3

- Equate the formula of the slope by 3

∴ $\frac{y-3}{x-5}=3$

- 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 - 12

To find point B chose any value for x and substitute it in the

equation 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 y

A point B is (1 , -9)

Learn more:

You can learn more about the slope of the linear equation in brainly.com/question/4152194

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