This document discusses how to calculate the slope of a line from two points on the line. It provides the formula for slope as the rise over the run, or (y2 - y1) / (x2 - x1). Several examples are worked through, finding the slopes of lines passing through different pairs of points. The key points are:
- Slope is the ratio of the vertical change (rise) to the horizontal change (run) between two points
- The formula to calculate slope from two points (x1, y1) and (x2, y2) is: (y2 - y1) / (x2 - x1)
- Slope can be positive, negative, zero
David John, Senior Senior Strategic Policy Adviser at AARP’s Public Policy In...ILC- UK
In July 2015, the Government began a consultation on changing how the UK incentivises private pension saving, and the Chancellor is expected to respond to this consultation in the Government’s annual Budget in March 2016.
The Future of Private Pension Saving, kindly supported by Age UK, brought together Parliamentarians, business, academics and industry experts to discuss how best the UK Government can incentivise private pension saving.
The debate was opened by initial remarks from Angela Rayner MP (Shadow Pensions Minister), Jackie Wells (Head of Policy and Research, Pensions and Lifetime Savings Association), Sarah Luheshi (Deputy Director, Pensions Policy Institute), and Yvonne Braun (Director, Long-Term Savings Policy, Association of British Insurers).
On Wednesday 27th January, David John, Senior Strategic Policy Adviser at AARP’s Public Policy Institute, and Deputy Director of the Retirement Security Project at the Brookings institute delivered a presentation on tax incentives for pension saving in the US context at an informal reception hosted by Age UK.
Discussions from this event contributed to a formal representation to the HM Treasury regarding Government policy on pensions tax relief and private pension saving.
Marketers have seen their jobs transformed over the past ten years. The transformation is happening again — but faster this time. According to The Economist Intelligence Unit's survey of 478 high-level marketing executives worldwide, sponsored by Marketo, more than 80% say they need to restructure marketing to better support the business. And 29% believe the need for change is urgent.
The Social Media Breakfast Fort Wayne event Ladies and Gentlemen Start Your Blogging
on June 28th 2011.
Connect with us at http://www.facebook.com/smbftw or on twitter at http://twitter.com/smbfw. Use the hashtag #smbfw to find others discussing the event on Twitter.
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
2. The slope of a non-vertical line is the
ratio of the vertical change (the rise) to
the horizontal change (the run) between
any two points on the line.
vertical change change in y
=
horizontal change change in x
3. Example 1 Find the slope of the line shown.
Write formula for
slope.
y2 – y1
m=
x2 – x1
4. If you know any two points on a line, you
can find the slope of the line without
graphing. The slope of a line through the
points (x1, y1) and (x2, y2) is as follows:
rise y2 – y1
slope = =
run x2 – x 1
5. Example 1: Finding Slope, Given Two Points
Find the slope of the line that passes through
A. (–2, –3) and (4, 6).
Let (x1, y1) be (–2, –3) and (x2, y2) be (4, 6).
y2 – y1 6 – (–3) Substitute 6 for y2, –3 for y1,
x2 – x1 = 4 – (–2) 4 for x2, and –2 for x1.
= 6 + 3 =9
4+2 6
=3 Simplify.
2
3
The slope of the line is 2 .
6. Example 2: Finding Slope, Given Two Points
Find the slope of the line that passes through
B. (1, 3) and (2, 1).
Let (x1, y1) be (1, 3) and (x2, y2) be (2, 1).
y2 – y1 1 – 3 Substitute 1 for y2, 3 for y1,
x2 – x1 = 2 – 1 2 for x2, and 1 for x1.
= −2 = –2 Simplify.
1
The slope of the line that passes through
(1, 3) and (2, 1) is –2.
7. WARM UP
Find the slope of the line that passes through
C. (3, –2) and (1, –2).
Let (x1, y1) be (3, –2) and (x2, y2) be (1, –2).
y2 – y1 –2 – (–2) Substitute −2 for y2, −2 for y1,
x2 – x1 = 1 – 3 1 for x2, and 3 for x1.
= −2 + 2 Rewrite subtraction as addition of
1–3 the opposite.
0
= –2 = 0
The slope of the line that passes through
(3, –2) and (1, –2) is 0.
8. WARM UP
Find the slope of the line that passes through
A. (3, 5) and (3, 1).
Let (x1, y1) be (3, 5) and (x2, y2) be (3, 1).
9. Helpful Hint
You can use any two points to find the
slope of the line.
The slope of a line may be positive, negative,
zero, or undefined. You can tell which of these
is the case by looking at the graphs of a line—
you do not need to calculate the slope.