Linear Equations

Chapter 2 Section 2Linear EquationsLesson essential question: How can you determine if an equation is linear? DefinitionsLinear Function: A function whose graph is a straight line.

Linear Equation: An equation that represents a linear functionThere are no exponents on x or y if the equation is lineari.e. y=3x+4.

Solution of Linear Equation: Any ordered pair that makes the equation true.i.e. (0,2) is a solution for y=x+2. More DefinitionsThe value of x is whatever we pick, so x is the Independent Variable. The value of y depends on whatever you pick for x. Therefore, we call y the Dependent Variable.

Independent Variable. Calls the shots. Dependent Variable. Notorious kiss-up. Interceptsy-intercept: the point at which the line crosses the y-axis. The x-intercept: the point at which the line crosses the x-axis.

Standard form of a linear equationThe Standard Form of a Linear Equation is Ax+By=C, where A, B, and C are real numbers, and A and B can not both be zero.

Graphing equations in the standard formSteps: Set x or y to 0 to find each intercept.(Set x=0 and solve for y and then vice versa)Use the intercepts to graph the equation.(Graph each intercept and connect the dots)Ex. Graph 3x+2y=120.

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SlopeSlope: the slope, is the ratio of the difference in y over the difference in x.How to calculate:

Slope continuedEx. Find the slope of the line through the points (1, 6) and (4, 5)

Slope-intercept formThe famous y=mx+b m=slopeb=the y-interceptFind the slope and the y-intercept of 4x-2y=10.Then graph the line.

Slope-intercept formGraph y=2x-5

Given a point and a slope

Writing an equation given two pointsWrite in slope-intercept form the equation of the line through (2,-3) and (-1, 2):

Properties of special slopes

m=0y is constantm is undefinedx is constant

m = m

Making Sense of writing equations of perpendicular linesWrite the equation of the line through each point and perpendicular to

a. (6, 1) b. (0,4)

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If you still have questions on todays lesson visitwww.PHSchool.comweb code: age 0775chapter 2, lesson 2Homework quiz web code: aga 0202

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