Question

graphing proportional relationships

Answer 1

To graph proportional relationships, you need to plot points that are in proportion to each other on a coordinate plane.

For example, if you have a proportional relationship where y is directly proportional to x with a constant of proportionality k, you can write this as y = kx. To graph this relationship, you can pick a few values for x, calculate the corresponding values for y using the equation y = kx, and then plot the points (x, y) on a graph.

For instance, let's say k = 2 and x = 1, 2, 3, 4.
When x = 1, y = 2(1) = 2
When x = 2, y = 2(2) = 4
When x = 3, y = 2(3) = 6
When x = 4, y = 2(4) = 8

Plotting these points on a graph, you will see that they lie on a straight line that passes through the origin (0,0) and extends indefinitely in both directions. This line represents the proportional relationship y = 2x.

You can also graph proportional relationships using a slope-intercept form, y = mx + b, where m is the slope, and b is the y-intercept. In a proportional relationship, the slope will be the constant of proportionality.

By plotting the points in a proportional relationship on a graph, you can visually see how they form a straight line that passes through the origin, indicating the proportional nature of the relationship.