1.1 Integers and Rational Numbers

11.2. Writing Linear Equations in Standard Form www.ck12.orgAx − Ax + By = C − AxBy −Ax +C=B By = −AB x + C BWhen you compare this form to slope-intercept form, y = mx + b, you can see that the slope of a standard formequation is −AB and the y−intercept is C B .The standard form of a linear equation Ax + By = C has the following:slope = −AB and y − intercept = C B .Example 3: Find the slope and y−intercept of 2x − 3y = −8.Solution: Using the definition of standard form, A = 2,B = −3, and C = −8.slope = −AB = −2−3 → 2 3y − intercept = C B = −8−3 → 8 3The slope is 2 3 and the y−intercept is 8 3 .Applying Standard Form to Real-World SituationsExample 4: Nimitha buys fruit at her local farmers market. This Saturday, oranges cost $2 per pound and cherriescost $3 per pound. She has $12 to spend on fruit. Write an equation in standard form that describes this situation.If she buys 4 pounds of oranges, how many pounds of cherries can she buy?Solution: Define the variables: x = pounds of oranges and y = pounds of cherriesThe equation that describes this situation is: 2x + 3y = 12If she buys 4 pounds of oranges, we substitute x = 4 in the equation and solve for y.218