Concepts

● Proportion is an equation stating that two ratios or rates are equivalent. It can be written in two ways: as two equal fractions $\frac{\mathrm{a}}{\mathrm{b}}\mathrm{ = }\frac{\mathrm{c}}{\mathrm{d}}$; or using a colon, a:b = c:d.

● Rate – A ratio that compares two quantities with different kinds of units.

● Rate of change – a rate that describes how one quantity changes in relation to another.

● Constant rate of change – two variables have a constant rate of change if the ratio of one variable to the other is proportional.

● Slope – rate of change between any two points on a line. 

slope = $\frac{\mathrm{change\; in\; y\; (rise)}}{\mathrm{change\; in\; x\; (run)}}\mathrm{ = }\frac{\mathrm{y}}{\mathrm{x}}$

Rules

1. Count the number of units that make up the rise of the line in the graph. It will be the numerator in the fraction (y).

2. Count the units that make up the run of the line. It will be the denominator (x).

Slope = $\frac{\mathrm{y}}{\mathrm{x}}$

Example

Select the correct slope of the graphed line.

$\frac{6}{5}$

$\frac{5}{6}$

-$\frac{6}{5}$

-$\frac{5}{6}$

Solution

1. Count or calculate the number of units that make up the rise of the line in the graph. 
7 - 2 = 5      y = 5

2. Count or calculate the units that make up the run of the line. 9 – 3 = 6     x = 6

slope = $\frac{\mathrm{change\; in\; y\; (rise)}}{\mathrm{change\; in\; x\; (run)}}\mathrm{ = }\frac{5}{6}$

Answer: $\frac{5}{6}$

Pre-requisite Skills

Coordinate Graphing (4.11.1)

Coordinate Graphing (4.11.2)