~adapted from Walch Education CONSTRUCTING FUNCTIONS FROM
GRAPHS AND TABLES
Slide 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
Slide 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.
Slide 5
Lets see Determine the equation that represents the
relationship between x and y in the graph to the right.
Slide 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
Slide 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.
