Allison can draw vertical segments from any two points on the line to the x-axis to form similar triangles. The vertical change divided by the horizontal change for any point on the line is the same, so the slope of the line is constant. The constant slope shows that the cost to rent an instrument is the same each month that Allison rents the instrument.
In Mathematics and Geometry, a proportional relationship is a type of relationship that produces equivalent ratios and it can be represented by the following mathematical equation:
y = mx
Where:
- y represents the y-variable.
- x represents the x-variable.
- m is the constant of proportionality.
In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;
Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope (m) = Change in vertical segment/Change in horizontal segment
Slope (m) = rise/run