Download Lesson 2.3--Graphing Linear Functions

Lesson 2.3--Graphing Linear Functions
Meteorologists can use linear functions to predict when a
hurricane will reach land.
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Functions with a constant rate of change are called linear
functions.
A linear function can be written in the form f(x) = mx + b,
where x is the independent variable and m and b are
constants.
The graph of a linear function is a straight line made up of
all points that satisfy y = f(x).
Example:
a.
b.
Example:
Graph the line with slope
that passes through (–1, –3).
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Recall from geometry that two points determine a line.
Often the easiest points to find are the points where a
line crosses the axes.
The y-intercept is the
y-coordinate of a point
where the line crosses
the y-axis.
The x-intercept is the
x-coordinate of a point
where the line crosses
the x-axis.
Example:
Find the intercepts of 4x – 2y = 16, and graph the line.
Linear functions can also be expressed as linear equations
of the form y = mx + b.
When a linear function is written in the form y = mx + b
the function is said to be in slope-intercept form
because m is the slope of the graph and b is the
y-intercept.
Notice that slope-intercept form is the equation solved
for y.
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Example:
Write the function –4x + y = –1 in slope-intercept form.
Then graph the function.
Write the function
Then graph the function.
in slope-intercept form.
An equation with only one variable can be represented by
either a vertical or a horizontal line.
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The slope of a vertical line is undefined.
The slope of a horizontal line is zero
.
Example:
Determine if each line is vertical or horizontal.
A. x = 2
B. y = –4 Lesson Quiz:
1. Determine whether the data could represent a linear
function.
2. For 3x – 4y = 24, find the intercepts, write in
slope-intercept form, and graph.
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3. Determine if the line y = -3 is vertical or
horizontal.
4. The bottom edge of a roof is 62 ft above the
ground. If the roof rises to 125 ft above ground
over a horizontal distance of 7.5 yd, what is the
slope of the roof?
HW: p. 110 22-36 even, 37, 42, 44, 52-54,
58-62, 64, 73-79 = 27 problems
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