FALL 2015 MATH 141
REVIEW OF STRAIGHT LINES
Given any two distinct points, there will be one and only one line that passes through both
points. If we are given the coordinates of both points, then we can use these coordinates to
obtain the following information:
• The slope of the line.
• The equation of the line.
• The y-intercept of the line.
• The x-intercept of the line.
The y-intercept of a line is the point where the line intersects the y-axis, while the xintercept is the point where the line intersects the x-axis.
The slope of a line tells us how much the quantity on the vertical axis changes when we
increase the quantity on the horizontal axis by 1 unit. We usually use the letter m to denote
the slope of a line.
If the line passes through the points (x1 , y1 ) and (x2 , y2 ), then
y2 − y1
m=
.
x2 − x1
Two lines are parallel if and only if they have the same slope.
The equation of a line (also called a linear equation) may be written in various forms.
If we know (i) the slope m, and (ii) a point (x1 , y1 ) that the line passes through, then we may
write down the point-slope form of the equation of the line, which is
y − y1 = m(x − x1 ).
If we know (i) the slope m, and (ii) the y-intercept (0, b), then we may write down the
slope-intercept form of the equation, which is
y = mx + b.
Sometimes we may write the equation such that x and y are on the same side. The most
general form of a linear equation is Ax + By + C = 0 where A, B, and C are constants with A
and B not both zero.
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REVIEW OF STRAIGHT LINES)
Solve the following problems to check how much you recall/understand.
1. Find the slope of the line that passes through the points (4, −3) and (6, 1).
2. Given the equation 2x + 3y = 4, answer the following questions.
(a) Is the slope of the line described by this equation positive or negative?
(b) As x increases in value, does y increase or decrease?
(c) As x decreases by 2 units, what is the corresponding change in y?
3. Find the equatlon of the line that passes through the point (−1, 3) and is parallel to the
line passing through the points (−2, −3) and (2, 5). Write the equation in slope-intercept form.