Module 5
Slope of Linear Equations in
Two Variables
Things to Know
 Slope
is a numerical value that measures
the steepness and direction of a line.
 It is calculated as the change in the yvalues divided by the change in the xvalues of two points on a line. It is often
referred to as “rise over run.”
 If 𝑥1 , 𝑦1 and 𝑥2 , 𝑦2 are two points, then
𝑦1 −𝑦2
𝑦2 −𝑦1
the slope is 𝑚 =
or
.
𝑥1 −𝑥2
𝑥2 −𝑥1






If an equation is in the form 𝑦 = 𝑚𝑥 + 𝑏, then
the coefficient of 𝑥, 𝑚, is the slope.
Vertical lines have an undefined slope.
Horizontal lines have a slope of 0.
We can graph a line knowing a point and its
slope.
Parallel lines have slopes which are the same.
The slopes of perpendicular lines are negative
reciprocals.
Finding slope given the graph
of a line on a grid
Find the slope of the line graphed below.
Finding slope given two points
on the line
Find the slope of the line passing through
the points −3, 7 and (2, −6).
Finding the slope of a line
given its equation
Find the slope of the line 2𝑥 − 4𝑦 = 3.
Find the slope of the line 𝑥 = 4.
Slopes of parallel and
perpendicular lines: Problem type 1
Consider the line 7𝑥 + 5𝑦 = −9.
(a) What is the slope of a line perpendicular
to this line?
(b) What is the slope of a line parallel to this
line?
Graphing a line given its equation
in slope-intercept form
Graph the line 𝑦 = −2𝑥.
Graphing a line through a
given point with a given slope
Graph the line with slope -3 passing through
the point(1, 5).