Question

consider the line through the origin and the point (5,7). A.) pretend that you do not already know that equations of lines have a particular form. Derive and explain an equation for the line of the form Y=m•x where M is a suitable number. In your explanation, attend to our definition of multiplication and explain why the equation holds for all points on the line (that have positive X and Y coordinates). B.) explain how to interpret M is the slope of the line. 

Answer 1

a) y = 1.4x

b) 1.4, that is, any time x changes by 1, y changes by 1.4.

Explanation:

A)

We want an equation in the following format:

y = mx

Point (5,7).

This means that when x = 5, y = 7. So

y = mx

7 = m*5

5m = 7

m = 7/5

m = 1.4

So the equation is:

y = 1.4x

B.) explain how to interpret M is the slope of the line.

The slope is how much y changes when x changes by 1.

In this case, it is 1.4, that is, any time x changes by 1, y changes by 1.4.