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SFM Productions Presents:
The first of many sagas in your seemingly never-ending
quest to master the
Pre-Calculus experience!
1.3
Linear Equations in Two Variables
Homework for section 1.3
p 33
21-25, 35,37, 57-61, 67,
91-97, 107, 115, 129, 131
Slope:
rise
run
Is the number of units a line rises or falls in a vertical direction per each ONE
unit of horizontal direction (left to right).
or
y2  y1
x2  x1
or
y
x
A vertical line has no slope. (Undefined)
A horizontal line has a slope of 0. (0 in numerator)
or
change in y
change in x
Equation of a line in slope-intercept form:
y  mx  b
* (x,y) is any point that makes the equation true. That means you can substitute in for x
and y to solve for m and b if necessary.
Equation of a line in point-slope form:
y  y1  m( x  x 1)
* (x1,y1) is any point that makes the equation true. That means you can substitute in for x
and y to solve for m and b if necessary.
*There is not much of a difference between the two formulas - use the one that makes you
feel good.
Equations of lines:
Ax  B y  C  0
General Form:
Veritcal line:
x  a
Horizontal line:
y  a
S lope- I ntercept f orm:
P oint- slope f orm:
y  mx  b
y  y1  m( x  x 1)
Parallel lines have slopes that are exactly the same.
Perpendicular lines have slopes that are negative reciprocals of each other.
Ex ample:
T he slope of the f irst line is 5 .
T he slope of a line perpendicular is -
1
5
Example:
Find an equation of the line that has a slope of 4 and passes through the point (-6, 2).
y  4x  2 6
Example:
Write, in general form, an equation of the line that passes through the
points (-2,1) and (3,2).
x 5 y 7  0
Example:
Find the slope of the line that is perpendicular to the line:
x through
 3 ythepoint
1 (1, Then find the equation of the parallel line that2goes
2)
3
2
4
m 
, y  
x 
2
3
3
You bought a machine thingi for $20,000. In 4 years the machine will be worth $10,000. Write a
linear equation that gives the value V of the machine after t years. Estimate the value of the
machine after a total of 10 years.
?
V  2 5 0 0 t  2 0 , 0 0 0 ; $  5 , 0 0 0
Other junk I
want you
guys to be
aware of……
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