Explore the foundational concepts of mathematics through engaging problem-solving and real-world applications in 7th grade.
When you plot a proportional relationship on a graph, it forms a straight line passing through the origin (0,0). The steepness of the line, called the slope, shows the rate of change between the two quantities.
The equation for a proportional relationship is \( y = kx \), where \( k \) is the constant of proportionality.
Graphs help you spot patterns and make predictions, like estimating the cost of multiple items or predicting travel distance over time.
\[y = kx\]
Plotting the cost of apples: If 1 apple costs $2, the line \( y=2x \) predicts the price for any number of apples.
A graph showing distance vs. time for a constant speed forms a straight line through the origin.
Graphs make it easy to see and predict proportional relationships.