Algebra 1H Glencoe McGraw-Hill J. Evans/C. Logan Standard Form And Word Problems Heath text, section 5.5

Slope-Intercept Form of a Linear Equation: y = mx + b Standard Form of a Linear Equation Ax + By = C variable terms are on the left side; the constant term is on the right side all coefficients are integers the leading coefficient is positive The GCF of all numbers is 1

Transform into standard form with integer coefficients. Clear the fraction. Put the x and y terms on the left hand side of the equation. This equation is in standard form because both x and y are on the same side and all coefficients are integers.

Ex. 1: Transform into standard form with integer coefficients. Clear the fraction. The x-term needs to have a positive coefficient. Put the x and y terms on the left hand side of the equation.

Ex. 2: Transform into standard form with integer coefficients. Multiply all terms by 100 to clear the decimals.

Substitute values for x, y, and m into the slope-intercept form. Clear the fraction. The coefficients of x and y must be integers. x and y need to be on the same side of the equal sign to be in standard form. The coefficient of x must be positive.

Ex. 4: Candy corn costs $2 per pound at the candy store and M&Ms cost $3 per pound. With $30 to spend, what are the different amounts of the two candies that you can buy? Let x = # pounds of M & Ms Let y = # pounds of candy corn Let 3x = VALUE of the M & Ms Let 2y = VALUE of the candy corn Value of M & Ms + Value of candy corn = Total Value 3x + 2y = 30

M & M’s (in pounds) Candy Corn (in pounds) Find the x- and y- intercepts. 3(0) + 2y = 30 y = 15 (all candy corn, no M & M’s) 3x + 2(0) = 30 x = 10 (all M&Ms, no candy corn) Each point on the line represents a combination of the 2 candies that would have a total cost of $30. Name some of the combinations.

Ex. 5: You are running for class president and have $48 to spend on publicity for your campaign. It costs $2 to make a campaign button and $1.20 to make a poster. Write an equation that represents the different numbers of buttons, x, and posters, y, that you could make. Let x = # of buttons Let y = # posters Let 2x = VALUE of the buttons Let 1.2y = VALUE of the posters Value of buttons + Value of posters = Total Cost 2x + 1.2y = 48 Find the x- and y- intercepts of the equation.

Number of Buttons Number of Posters Each point on the line represents a combination of posters and buttons with a total value of $ x y

This equation is in standard form. What can we learn by looking at it in slope-intercept form? Look back at the table of values to see this pattern. y-intercept of the graph

Ex. 6: Dogs sell for $50 and cats sell for $30 at Pets-R-Us. Sales figures for the busy holiday shopping season showed that the store received $3300 total for dog and cat sales in one weekend. Write an equation to describe the sales that weekend of dogs, x, and cats, y. Let x = # dogs Let y = # cats Let 50x = VALUE of dogs Let 30y = VALUE of cats Value of dogs + Value of cats = Total Value 50x + 30y = 3300 Find the x- and y-intercepts of the equation.

x y -5+3