How do you use linear graphs to problem solve?

Question

Nathan Axel · Accepted Answer

If you have a linear graph you can find corresponding values from one axis (or scale) to another.

This is most easily seen by an example:

Here we have the linear graph showing the relationship between temperatures measured in Fahrenheit and in Celsius.

If you wanted to know what #50^o#C was in the Fahrenheit scale, you would follow a vertical line up from the #50# on the Celsius axis, to the linear graph line, then move horizontally across to the Fahrenheit axis to get a reading of (approximately) a lit more than #120^o# F. (See the light blue lines for this procedure).

If your problem was to convert a temperature in Fahrenheit to Celsius you would simply reverse the process ( horizontal across to the linear graph line from the Fahrenheit temperature and then horizontally down to the Celsius equivalent.

The accuracy of your result will of course depend upon how accurate your graph has been drawn.

Abigail Allen · Answer

undefined Linear graphs are used in problem-solving by visually representing relationships between two variables. To use linear graphs for problem-solving, follow these steps:

1. Identify the variables: Determine the two variables involved in the problem and assign them to the x-axis and y-axis on the graph.

2. Plot points: Plot the given data points on the graph. Each data point represents a pair of values for the two variables.

3. Draw the line: Connect the plotted points with a straight line. This line represents the trend or relationship between the variables.

4. Interpret the graph: Analyze the graph to understand the relationship between the variables. Determine if the relationship is positive (increasing), negative (decreasing), or neutral (no change). Also, assess the slope of the line to understand the rate of change between the variables.

5. Use the graph to solve problems: Once the graph is constructed, use it to predict or estimate values, find solutions to equations, or make decisions based on the relationship between the variables.

Overall, linear graphs provide a visual tool for problem-solving, allowing for a better understanding of relationships between variables and facilitating the analysis of data to reach conclusions or make informed decisions.