Exercise 11 Page 159

Consider the given graph.

We want to find if x and y are in a proportional relationship. To do so, remember that when two quantities are proportional, the relationship can be represented by the following equation. y=mx Here, m is the constant of proportionality. The graph of this equation is a line with a slope m that passes through the origin. Notice that the given line passes through the origin. This means that x and y are in a proportional relationship. To find the equation of the line, we will use the Slope Formula to obtain m. m = y_2-y_1/x_2-x_1 Let's use the points ( 0, 0) and ( 1, 4) in the Slope Formula.

Finally, we can substitute the slope into the equation of the proportional relationship. y=4x

Extra

Linear Equations

A linear equation is an equation whose graph is a line.

This type of equation contains at least one linear term and any number of constants. Let's see a few examples! & y=2x+1, & 3x=6 +3, & 2y+x=4 For those of you who are interested in learning more about the different types of linear equations and their graphs, you can read more about them on the following pages.

• Graphing Linear Equations Using a Table of Values
• Writing a Linear Equation in Standard Form