(Section 7)
A thorough knowledge of graphing linear
and non-linear equations is extremely helpful for a visual understanding
of many basic calculus concepts. Therefore, it is very important that any
student beginning a study of calculus have a firm comprehension of the
following graphing ideas.
Straight Lines
Straight lines:
y = 5 a horizontal line through y = 5 (a linear
function of x)
x = -7 a vertical line through x = 5 (a linear function
of y, but not a linear function of x)
Point-Slope Form
y - y1 = m(x - x1) a line through
(x1,y1) with a slope of m
y - 3 = 6(x + 2) a line through (-2,3) with a
slope of 6
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Slope-Intercept Form
y = mx + b a line through (0,b) with a slope of m
y = -2x + 8 a line through (0,8) with a slope of
-2
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Taylor Form
a line through 
with a slope of m
a line through (3,2) with a slope of  .
This form is useful when entering an equation in a
graphing calculator since all the equation must be entered to the right of
the equal sign.
Parallel Lines
Two lines are parallel if and only if they have equal
slopes but different y-intercepts:
Perpendicular Lines
Two lines are perpendicular if and only if they have
slopes whose product is -1.
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Warning: Sometimes these
lines may not appear to be perpendicular. Many graphing calculator windows
are not square, but instead rectangular. If windows are not square, the
lines with negative reciprocal slopes will not appear perpendicular.
Check Your Understanding:
(Remember to write down your answers.)
Are these lines perpendicular, parallel
or neither?
1. y = 3x + 8 and 3x + y = 10
2. 4x + 3y = 12 and 3x - 4y = 24
3. x - y = 12 and x - y = 15
4. Write the equation, in point-slope
form, of a line through (-2,1) with a slope of 2.
5. Write the equation, in
slope-intercept form, of a line parallel to y = 3x - 8 that passes through
(2,1). Enter this equation in your calculator and check to see that (2,1)
is a solution to your equation.
6. Write the equation, in point-slope
form, of a line perpendicular to x + 2y = 8 that passes through the
origin. Graph both lines on a square window to check to see that the lines
are visually perpendicular.
7. Write the equation, in Taylor form,
of a line parallel to 3x - 2y = 7 that passes through (3,1). Enter this
equation in your calculator and check to see that (3,1) is a solution to
your equation.
Review of Distance Formula, the
midpoint of a segment, and the angle of elevation.
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