Write the linear equation such that each point on its graph has an ordinate 4 times its abscissa.

To find the linear equation where each point on its graph has an ordinate (y-value) that is four times its abscissa (x-value), we can start by using the relationship between x and y. The term "ordinate" refers to the y-coordinate, while "abscissa" refers to the x-coordinate. So, if we denote the abscissa as x, the ordinate can be expressed as 4x.

Formulating the Equation

Based on the relationship given, we can write the equation as:

y = 4x

Understanding the Components

In this equation:

• y represents the ordinate (the vertical position on the graph).
• x represents the abscissa (the horizontal position on the graph).
• The coefficient 4 indicates that for every unit increase in x, y increases by four units.

Graphing the Equation

When you graph this equation, you'll notice that it is a straight line that passes through the origin (0,0) and has a slope of 4. This means that for every step you take to the right along the x-axis, you move four steps up on the y-axis. The line will rise steeply, reflecting the strong relationship between x and y.

Example Points on the Line

To visualize this further, let’s calculate a few points that lie on the line:

• If x = 1, then y = 4(1) = 4. So, the point (1, 4) is on the line.
• If x = 2, then y = 4(2) = 8. Thus, the point (2, 8) is also on the line.
• If x = -1, then y = 4(-1) = -4. Therefore, the point (-1, -4) is included as well.

Conclusion

The linear equation that describes the relationship where each point on its graph has an ordinate four times its abscissa is simply y = 4x. This equation not only defines the line but also helps us understand how y changes in relation to x. By analyzing the slope and plotting points, we can visualize the linear relationship effectively.