Question

The slope of diagonal OA IS__,
and its equation is__

Answer 1

`(a)\ m = (4)/(3)` --- slope of OA

`(b)\ y = (4)/(3)x` --- the equation

Explanation:

Given

The attached graph

Solving (a): Slope of OA

First, we identify two points on OA

`(x_1,y_1) = (0,0)`

`(x_2,y_2) = (3,4)`

So, the slope (m) is:

`m = (y_2 -y_1)/(x_2 - x_1)`

This gives:

`m = (4-0)/(3-0)`

`m = (4)/(3)`

Solving (b): The equation

This is calculated as:

`y = m(x - x_1) + y_1`

Recall that:

`(x_1,y_1) = (0,0)`

`m = (4)/(3)`

So, we have:

`y = (4)/(3)(x - 0) + 0`

`y = (4)/(3)(x)`

`y = (4)/(3)x`