1.1 Integers and Rational Numbers

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$Lesson 2a – Assessment - Scottsdale Community College - Math Blog$

www.ck12.org Chapter 11. More on Linear Functions11.2 Writing Linear Equations in Standard FormAs the past few lessons of this chapter have shown, there are several ways to write a linear equation. This lessonintroduces another method: standard form. You have already seen examples of standard form equations in aprevious lesson. For example, here are some equations written in standard form.0.75(h) + 1.25(b) = 307x − 3y = 212x + 3y = −6The standard form of a linear equation has the form Ax + By = C, where A,B, and C are integers and A and B arenot both zero.Example 1: Rewrite y − 5 = 3(x − 2) in standard form.Solution: Use the Distributive Property to simplify the right side of the equationy − 5 = 3x − 6Rewrite this equation so the variables x and y are on the same side of the equation.y − 5 + 6 = 3x − 6 + 6y − y + 1 = 3x − y1 = 3x − y, where A=3, B=-1, and C=1.Example 2: Rewrite 5x − 7 = y in standard form.Solution: Rewrite this equation so the variables x and y are on the same side of the equation.5x − 7 + 7 = y + 75x − y = y − y + 75x − y = 7,where A=5, B=-1, and C=7.Finding Slope and Intercept of a Standard Form EquationSlope-intercept form of a linear equation contains the slope of the equation explicitly, but the standard form doesnot. Since the slope is such an important feature of a line, it is useful to figure out how you would find the slope ifyou were given the equation of the line in standard form.Begin with standard form: Ax + By = C.If you rewrite this equation in slope-intercept form, it becomes217
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
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1.1 Integers and Rational Numbers

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