1. 15 + x = 100, solve for x. 2. Given the data below, what is the probability

that a person will buy a bicycle rather than a scooter.

3. x – 30 = -50, solve for x4. Round the given number to the hundredths

place, 215.6977 5. Round the given number to the ones place,

215.6977

  Person A Person B Person C

Person D

Person E

Scooter x x x  Bicycle   x     x

Graphing Activity

• Get into groups of 2-3 students.• Each group will get a starting point and a

slope• Your task is to find the next point in your line• Then check your point by finding the slope

between the starting point and your point

Standard Formx- and y-intercepts

November 28/29, 2011

What is a Linear Equation?

• In a graph, Linear equations will be a line• In a table, Linear equations will have an

arithmetic pattern• In an equation, Linear equations can be

written as slope-intercept form, y = mx + b, and standard form, Ax + By = C

Standard Form

• To be a linear equation, an equation must be able to be written in the form Ax + By = C

• This is called Standard Form• A, B and C are always integers (no fractions)• A must be positive• Is this in Standard Form?• 3x + 5y = 12• 1/2x – y = 12• -2x + 5y = 30

How to change an equation to Standard Form

• Write ⅔x = –6y + 1 in standard form. • Identify A, B, and C.• ⅔x = –6y + 1 Original equation• + 6y +6y___ Add 6y to each side.• ⅔x + 6y = 1• 3(⅔x + 6y = 1) Multiply each side by 3 • 2x + 18y = 3• So, A = 2, B = 18, and C = 3.

Example 2• Put 2 + 5y = –x in Standard form and identify A, B and C.

• 2 + 5y = –x  Original equation• 2 + 5y = –x  Add x to each side.•       + x   + x• 2 + 5y + x = 0 Subtract 2 from each side.• 2 + 5y + x = 0• – 2 – 2 • x + 5y = –2 Simplify. • A = 1, B = 5, and C = –2.

Now You Try

• Can this be written in Standard Form?• If yes, change to Standard Form.• y = 2x + 5• 7x = 4y – 6• y = x² + 6• ¾x + ½y = 12

Practice

• Work on problems 1-9• You have 15 minutes.

Finding x- and y-intercepts

• x-intercept– where a line crosses the x-axis– when y = 0– (x, 0)

• y-intercept– where a line crosses the y-axis – when x = 0– (0, y)

Finding the x-intercepts and y-intercepts (continued)

• Which is the intercepts?

• A x-intercept is 0; y-intercept is 6.

• B x-intercept is –3; y-intercept is 0.

• C x-intercept is –3; y-intercept 6.

• D x-intercept is 6; y-intercept is –3.

y

x O

Graphing using x-intercepts and y-intercepts

To find the x-intercept, let y = 0 5x – y = 10 Original Replace y with 0. 5x – 0 = 10 Simplify.5x = 10Divide each side by 5.• x = 2 • x-intercept is (2, 0)

To find the y-intercept, let x = 0. 5x – y = 10 OriginalReplace x with 0.5(0) – y = 10 Simplify. –y = 10 Multiply each

side by –1.y = –10y-intercept is (0, -10)

Graph 5x – y = 10 using the x- and y-intercepts.

Finding x- and y-interceptsNow you try

• y – 3x = -1• 5x + 3y = 15• x + 4y = -8

Finding x- and y-interceptsNow you try

Practice

• Work on problems 10-18• You have 15 minutes