Question

The linear equation of the initial (red ) incline would be y = __x +__

Answer 1

`y=\underline {1.5}x+\underline 0`

Explanation:

From the graph,

The initial red incline is a straight line passing through the origin.

So, a straight line passing through the origin is of the form:

`y=mx+0`

Where, 'm' is the slope.

Now, the slope of a given as the change in y value to change in x value.

Consider the two end points of the red line (0, 0) and (4, 6).

The slope with two points
`(x_1,y_1)\ and\ (x_2,y_2)` on the line is given as:

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

Plug in
`x_1=0,y_1=0,x_2=4,y_2=6`. Therefore, slope is:

`m=(6-0)/(4-0)\\m=(6)/(4)=1.5`

Hence, the equation of the initial red incline is:

`y=\underline {1.5}x+\underline 0`