2. ~adapted from Walch Education CONSTRUCTING FUNCTIONS FROM GRAPHS AND TABLES

3. Linear Equations The graph of a linear equation is a straight line. Linear equations have a constant slope, or rate of change. Linear equations can be written as functions. The general form of a linear function is f (x) = mx + b, where m is the slope and b is the y-intercept. The y-intercept is the point at which the graph of the equation crosses the y-axis. The slope of a linear function can be calculated using any two points, (x 1, y 1 ) and (x 2, y 2 ): the formula is

4. Exponential Equations Exponential equations have a slope that is constantly changing. Exponential equations can be written as functions. The general form of an exponential function is f(x) = ab x, where a and b are real numbers. The graph of an exponential equation is a curve. The common ratio, b, between independent quantities in an exponential pattern, and the value of the equation at x = 0, f(0), can be used to write the general equation of the function: f(x) = f (0) b x.

5. Let’s see… Determine the equation that represents the relationship between x and y in the graph to the right.

6. The solution Identify points from the curve. From the graph, three points are: (0, –4), (1, –1), and (2, 2). Find the slope of the line, using any two of the points. Using the points (0, –4) and (1, –1), the slope is 3 Find the y-intercept. The y-intercept can either be found by solving the equation f(x) = mx + b for b, or by finding the value of y when x = 0. On the graph, we can see the point (0, –4). The y-intercept is –4

7. Use the slope and y-intercept to find an equation of the line The relationship can be represented using the equation f (x) = 3x – 4.

8. ~dr. dambreville THANKS FOR WATCHING!