Final answer:
To find the equation of a line given two points, calculate the slope using the formula (Y2 - Y1) / (X2 - X1) and then use the slope and one point to find the y-intercept for the slope-intercept form y = mx + b. A calculator can simplify this process using regression functions.
Step-by-step explanation:
Finding the equation of a line when given two points involves using the formula for slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. To calculate the slope, represented by the letter m, use the formula m = (Y₂ - Y₁) / (X₂ - X₁) where (X₁, Y₁) and (X₂, Y₂) are the coordinates of the two given points. Once you have the slope, use one of the points to solve for b, the y-intercept, by plugging the slope and the coordinates of the point into the slope-intercept equation.
If using a calculator or computer software, input the coordinates of the two points and use the regression function to calculate the equation of the line. After finding the equation, you can add it to your scatter plot to visualize the line that best fits the data. The equation should be rounded to four decimal places for accuracy.
In practice test solutions, various linear equations are derived from different situations, such as tallying total hours required based on square footage, calculating the total payment with the number of students, or total cost of attendance over the years. Each scenario provides a practical example of how to create a linear equation using two sets of related data points.