Question

Part 1: Describe what the variable m represents on the graph.Part 2: Explain how this graph demonstrates how the equation y = mx can be derived from the two points (1, m) and (x, y)

Answer 1

From the given graph,

we get that two points (1,m) and (x,y) is on the line.

To find that the variable m that represents on the graph,

we know that slope of a line passing through two points (x1,y1) and (x2,y2) as,

`Slope=(y2-y1)/(x2-x1)`

To find slope of the given line.

Line passes through the points, (0,0) and (1,m)

we get,

`Slope=(m-0)/(1-0)`

`\text{Slope}=m`

Hence m is the slope of the line.

The line passes through the (0,0) and (1,m)

The equation of line is,

`(y-m)/(0-m)=(x-1)/(0-1)`

we get,

`y-m=m(x-1)`
`y-m=mx-m`
`y=mx-m+m`

we get,

`y=mx`

The equation of the line is,

`y=mx`

Hence derived.

The given straight line has slope m and passes through the origin.

y intercept is 0.

It verified the equation of the straight line y=mx.