1. Math 025 Section Slope

2. Objectives: to find the x- and y-intercepts of a straight line
to graph a line using x- and y-intercepts
to find the slope of a straight line
to determine from their slopes whether two lines are parallel
to graph a line using the slope and the y-intercept

3. The graph of 2x + 3y = 6 is shown below.
The graph crosses the x-axis at the point (3, 0) y
This point is called the x-intercept of the graph
(0, 2)
(3, 0) x
The graph crosses the y-axis at the point (0, 2)
This point is called the y-intercept of the graph
Note:
y = 0 at the x-intercept
x = 0 at the y-intercept

4. Find the x-intercept and y-intercept for x – 2y = 4
Then graph the line
x-intercept:
Let y = 0 y
x – 2(0) = 4
x = 4
x-intercept:
(4, 0)
y-intercept:
Let x = 0 x
0 – 2y = 4
-2y = 4
y = -2
y-intercept:
(0, -2)

5. The slope of a line is a measure of the slant of the line.
It is sometimes described as: Slope = rise run
It can also be described as: Slope = change in y change in x
positive slope
zero slope
negative slope
undefined slope

6. D y
slope = m =
D x
If you move in a negative direction to find Dy or Dx, use a negative number to describe that movement.
Red line: -3
m =
= -3 1
Blue line: 5
m = 7

7. Find the slope of the line containing the given points
You can find the slope of a line without graphing it if you know two points, P1(x1, y1) and P2(x2, y2), that are on the line.
y2 – y1
slope formula:
m =
x2 – x1
Find the slope of the line containing the given points
-3 – 3 -6 -3
P1(1, 3) P2(5, -3)
m = = =
5 – 1 4 2
-3 – 2 -5
P1(-1, 2) P2(-1, -3)
m = = =
Undefined
-1 – (-1)

8. The slopes are the same, so the lines are parallel.
Parallel lines have the same slope
Determine whether the line through P1 and P2 is parallel to the line through Q1 and Q2
– 6
P1(4, -5) P2(6, -9)
mP = =
= -2
-4 – – 1 -8
Q1(5, -4) Q2(1, 4)
mQ = =
= -2 4
The slopes are the same, so the lines are parallel.

9. The slopes are negative reciprocals, so the lines are perpendicular.
Perpendicular lines have slopes that are negative reciprocals of each other
Determine whether the line through P1 and P2 is perpendicular to the line through Q1 and Q2
P1(-4, -5) P2(-6, -9)
mP = =
= 2
1 – -4 -1
Q1(-4, 5) Q2(4, 1)
mQ = = = 8 2
The slopes are negative reciprocals, so the lines are perpendicular.

10. Determine whether the lines through P1 and P2 and through Q1 and Q2 are parallel, perpendicular or neither
– 3
mP = =
P1(5, 1) P2(3, -2)
– 0 -2
Q1(0, -2) Q2(3, -4)
mQ = = 3
Perpendicular
– 3
mP = =
P1(1, -1) P2(3, -2)
-5 – -6
Q1(-4, 1) Q2(2, -5)
mQ = =
= -1 6
Neither

11. The slope is the coefficient of x
(-2, 5)
y = -3x
Notice that the above equation can be used to determine the slope and the y-intercept without having seen the graph.
(2, -1)
The slope is the coefficient of x
– 2
6 -4 -3
m = = = 2
The y-coordinate of the y-intercept point is the constant at the end of the equation.
y-intercept = (0, 2)

12. Slope = m y-intercept = (0,b)
Slope-intercept form of an equation y = mx + b
Slope = m y-intercept = (0,b)
Find the slope and the y-intercept of each equation
y = -3x
2x – 5y = 10
-5y = -2x + 10
y = 2x
slope =
slope =
y-intercept = (0,5)
y-intercept = (0, -2)

13. Graph: y = -2x
slope = -2/5
y-intercept = (0, 4)
1st: Graph the y-intercept point
2nd: Use the slope movements to find another point
3rd: Draw the line

14. Graph:
2x – 3y = -3
-3y = -2x – 3
y = 2x
slope = 2/3
y-intercept = (0, 1)