4-5B Write an Equation in Standard Form and in Slope-Intercept Form Algebra 1 Glencoe McGraw-Hill Linda Stamper

Remember: slope-intercept form and point-slope form

and the constant term is on the right side. In this lesson you will write the equation of a line given in point-slope form into standard form. Do you remember the standard form for a linear equation? Ax + By = C In standard form, the variable terms are on the left side of the equal sign and the constant term is on the right side. The A is the coefficient of the x term while the B is the coefficient of the y term! C represents a constant.

In standard form A > 0, and A and B are not both zero and A, B, and C are integers with a greatest common factor of 1. Explain why the following equations are NOT considered to be in standard form. x and y need to be on the left side of equal sign. x term comes before the y term. “A” needs to be greater than or equal to one. “A” is not an integer. GCF of A, B, and C is not 1.

What do the instructions “integer coefficients” mean? Write in standard form with integer coefficients. What do the instructions “integer coefficients” mean?

Natural or Counting Numbers REAL NUMBERS Integers: Whole numbers and their opposites (this means positive and negative whole numbers). ex: … ־ 4, 3, 2, 1, 0, 1 ־, 2 ־, 3 ־, 4 … Whole Numbers: Natural Numbers and zero. ex: 0,1,2,3… Natural or Counting Numbers ex: 1,2,3,4,…

Write in standard form with integer coefficients. What do the instructions “integer coefficients” mean? Positive or negative whole numbers in front of the variables. NO FRACTIONS or DECIMALS as COEFFICIENTS!

Copy in your spiral notebook! Write in standard form with integer coefficients. How can you get an integer coefficient for x? Could you use the reciprocal of Multiply each side of the equation by 4 to clear the denominator. No, using the reciprocal just gives the fraction to the other variable! Distribute. Subtract 20 and simplify. Add 5x to both sides. Copy in your spiral notebook!

Write in standard form with integer coefficients. Multiply each side of the equation by 5 to clear the denominator. Distribute. Add 15 and simplify. Subtract 3x to both sides. Undo the negative value for “A”.

Write in standard form with integer coefficients. Example 1 Example 2 Example 3 Example 4

Write in standard form with integer coefficients. Example 1 Example 2

Write in standard form with integer coefficients. Example 3 Example 4

Next in this lesson you will write the equation of a line given in point-slope form into slope-intercept form. slope-intercept form

Copy in your spiral notebook! Write in slope-intercept form. Write the equation. Distribute the slope. Add 2 to each side and simplify. Copy in your spiral notebook!

Another method: You could undo the fraction! Write in slope-intercept form. Write the equation. Undo the fraction. Simplify. Another method: You could undo the fraction! Copy in your spiral notebook!

Write in slope-intercept form. Example 5 Example 6 Example 7

Write in slope-intercept form. Example 8 Example 9 Example 10

Summary Equations of Lines

Homework 4-A12 Pages 223−224 # 26–41,48–54.