Final answer:
To graph a line on a graphing calculator, input the slope-intercept form of the equation with the given slope and point.
Step-by-step explanation:
To graph a line with a given point and slope using a graphing calculator, you will follow several steps. Knowing the slope is crucial as it determines the steepness of the line, and having a specific point allows you to place the line accurately on the graph. Moreover, using two points that are far apart can minimize the error while determining the slope due to the proportionately smaller interval.
- First, identify the slope of the line, which is the ratio of the rise over the run. In Figure A1, the slope is 3, meaning for every increase of 1 on the horizontal axis there is a rise of 3 on the vertical axis.
- Locate the given point on the graph; this could be the y-intercept or any other point on the line. In our case, the y-intercept is 9, which means that when x=0, y=9.
- Input the slope-intercept form of the equation of the line (y = mx + b) into the calculator, replacing m with the slope and b with the y-intercept value if it's given or any other point to solve for b.
- Use the graph function on the calculator to display the line, or if working with data points, input the data to create a scatter plot and then use the regression function to find the equation-of-the-line and add the least-squares regression line to your scatter plot. The symbol ˇ (y-hat) is often used in statistics to represent the predicted values of y based on the regression equation.
- Finally, review the graph to ensure it passes through the given point with the correct slope.
It is important to check the accuracy of the plotted line against the known data points to ensure it precisely represents the given slope and intercepts on the graph.