Slope-Intercept Form

The equation of a line can be written in slope-intercept form as y equals m x plus b. Here, m is the slope, and b is the y-coordinate of the point where the line crosses the y-axis, called the y-intercept.

To understand this, let's look at the relationship between the Celsius and Fahrenheit temperature scales. Students heat a liquid and record the temperatures at regular intervals in both Celsius and Fahrenheit.

They plot the Celsius values on the x-axis and the Fahrenheit values on the y-axis. The data points form a straight line, showing a linear relationship.

This means the rate of change is constant, with Fahrenheit increasing by 1.8 degrees for every 1-degree increase in Celsius. So, the slope is 1.8. The line crosses the y-axis at 32. This means that when Celsius is 0, Fahrenheit is 32. So, the y-intercept is 32.

Now we can substitute these values into the slope-intercept form. The equation becomes F equals one point eight C plus thirty-two.

This equation uses slope-intercept form to convert Celsius temperatures to Fahrenheit.