Section 3.7 p.189
Graphing Linear Equations
 Definitions:
 Cartesian Coordinate Plane – a graph
 X – axis –
 the horizontal axis of a coordinate plane
 Y – axis –
 the vertical axis of a coordinate plane
Graphing Linear Equations
 Definitions:
 Origin –
where the two axes meet (0,0)
 Ordered pair –
 x and y values of a point on a graph
 Also called a point of a set of coordinates
 Quadrants – the four sections that the x and y
axes divide the coordinate plane into – named I, II,
III, and IV
Coordinate Plane
 Identify
 Origin
 Y-axis
 X-axis
 Quadrants I, II, III, and IV
“Rise Up Run Out”
 Slope
 “Steepness”
 What are some examples where slope is a factor?
grade of a road, incline of wheelchair ramp, pitch of a roof,
etc.
Slope of a Line
 Slope
m=


𝑟𝑖𝑠𝑒
𝑟𝑢𝑛
=
=
=
𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑐ℎ𝑎𝑛𝑔𝑒
ℎ𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝑐ℎ𝑎𝑛𝑔𝑒
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑦 𝑐𝑜𝑜𝑟𝑑𝑖𝑛𝑎𝑡𝑒𝑠
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑥 𝑐𝑜𝑜𝑟𝑑𝑖𝑛𝑎𝑡𝑒𝑠
(𝑦2− 𝑦1 )
(𝑥2 −𝑥1 )
 Pick any two points on a line to compute the slope
Determine the slope of a line given the
coordinates of two points on the line
 Given A (-1,2) and B (4, -2)
 Find the slope of line AB
𝑚=
4
−
5
Find the slope of the segment below
 (5, 4) and (3, -1)
 Slope =
 m=
=
 Positive vs. negative slope
 Positive slope- rises to the right
 Negative slope- falls to the right
Slope
 Horizontal line
 Slope = ∆y =
∆x
 Vertical line
 Slope = ∆y =
∆x
0 =0
∆x
∆y = undefined
0
 Given C (4, 0) and D (4, -2)
 Find the slope of line CD
2
0
 𝑚 = undefined
Slope of a Line
 Special cases:
 x=4
 What will this slope be?
 y=-3
 What will this slope be?
Slope-Intercept Form
 𝑦 = 𝑚𝑥 + 𝑏
 𝑚 = 𝑠𝑙𝑜𝑝𝑒 𝑎𝑛𝑑 𝑏 = 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡
 Given 𝑦 =
2
𝑥
3
− 5,
 What is the slope?

2
3
 What are the coordinates of the y-intercept?
 (0, -5)
Graph y =
2
x
3
-5
Point-Slope Form
 𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1 )
 𝑚 = 𝑠𝑙𝑜𝑝𝑒 𝑎𝑛𝑑 𝑥1 , 𝑦1 𝑖𝑠 𝑎 𝑝𝑜𝑖𝑛𝑡 𝑜𝑛 𝑡ℎ𝑒 𝑙𝑖𝑛𝑒
 Given point A (3, 5) on the line with a slope of -1, find
the equation of the line in point-slope form.
 𝑦 − 5= −1(𝑥 − 3)
 Write the equation of this line in slope-intercept form.
 𝑦= −𝑥 + 8
 What is the equation of a line in point-slope form
passing through point A(-2,-1) and B(3, 5)?
 First find the slope; 𝑚 =
6
5
 Then plug one of the points into the point-slope form
of the line; 𝑦 − 5 =
6
5
𝑥−3
More Practice
 What is the equation of a line in slope intercept form







with slope of -2 and a y-intercept of (0, 5)?
𝑦 = −2𝑥 + 5
In point-slope form?
y- 5 = -2(x-0)
What is the equation in point-slope form of the line
through (-1, 5) with a slope of 2?
𝑦 − 5 = 2(𝑥 + 1)
In slope-intercept form?
𝑦 = 2𝑥 + 7
Homework
 P.194-195 #9-41 odd
 Additional Practice
 13-2 Slope of a Line worksheet
 How do you think the slopes of parallel lines compare?
 What about perpendicular lines?
Slopes of Parallel Lines (GSP)
Slopes of Perpendicular Lines (GSP)
3.8 Slopes of Parallel and Perpendicular Lines
 Two non-vertical lines are parallel if and only if their
slopes are equal.
 (parallel lines have the same slope)
 Two non-vertical lines are perpendicular if and only if
the product of their slopes is -1
 (slopes of perpendicular lines are negative reciprocals
of each other)
 m1 *m2 = -1 or m1= -1/m2
 Are the two lines below parallel?
 y= -3x +4 and y=-3x -10
 y= 4x-10 and y=2x-10
2
3
2
3
 y= x +5 and y = x +7
 Are the two lines below perpendicular?
1
4
4
x
3
 y= 4x – 2 and y= - x +5
 y=
 y=
3
- x +4 and y=
4
3
4
x -10 and y=
4
3
+4
+5
 Given a line through points (5,-1) and (-3, 3), find the
slope of all lines
 A. parallel to this one
 B. perpendicular to this one
 Slope = (-1 – 3)/ (5 – (-3)) = -4/8 = -1/2
 A. slope = -1/2
 B. slope = 2
Are the two lines below
perpendicular?
 (-4, 2) and (0, -4)
 (-5, -3) and (4, 3)
Homework
 p.201-203 #7-10, 15-18, 23, 25, 31, 33
 13-3 Parallel and Perpendicular Lines worksheet
 13-7 Writing Linear Equations worksheet #11-23 odd,
24-26 all
Find the distance between points A and B
A
Two points in a horizontal line
Distance = absolute value of the difference in the
x-coordinates
Distance=|-2 – 2| = 4 or |2 – (-2)| = 4
B
Find the distance between points A and B
A
B
Two points in a vertical line
Distance = absolute value of the difference in the
y-coordinates
Distance=|-8 – 3| = 11 or |3 – (-8)| = 11
 What about two points that do not lie on a horizontal
or vertical line?
 How can you find the distance between the points?
 The distance between two points is equal to the length
of the segment with those points as the endpoints
The Distance Formula
 The distance between points (x1, y1) and (x2, y2) is given by:
 d=
 Find the distance between (0, 0) and (7, 24)
 d=
 d = 25
Midpoint Formula Review
 Find the midpoint of the line segment with endpoints
(4, 7) and (-2, 5)


𝑥1+𝑥2
2
4+(−2)
2
 (1, 6)
,
,
𝑦1+𝑦2
2
7+5
2
Class work
 13-1 Distance Formula worksheet
 13-5 Midpoint Formula worksheet