Presentation on theme: "Lines, Lines, Lines!!! ~ Standard Form"— Presentation transcript:
1Lines, Lines, Lines!!! ~ Standard Form Another equation of thesame line.
2What we Have Learned so far…. Slope Intercept FormWhere m is the slope and b is the intercept
3What we Have Learned so far…. Point-Slope FormWhere m is the slope and are a point on the line.
4We will use our prior knowledge of Slope-Intercept Form&Point-Slope FormTo learn about the Standard Form of a Line:Ax + By = C
5Standard Form The Standard Form of a Linear Equation is Ax + By = C Where A ≥ 0,&A and B are not both zeroA, B, and C are integers whose greater common factor is 1.
6Standard Form Notice that: x and y have exponents of 1 The Standard Form of a Linear Equation isAx + By = CNotice that:x and y have exponents of 1x and y are not multiplied togetherx and y do not appear in denominators, exponents, or radicals
7Examples of Standard Form These Equations are not in Standard Form:1/2x + 2/3y = 612x – 36y = 105ix + 7py = -29These Equations are in Standard Form:2x + 5y = 7x – y = - 101000x + 75y = 6
8Question:Is the equation 4x + 7y = -10 a linear equation? Explain why.This equation is a linear equation because it is in standard form with A = 4, B = 7, and C = –10.Is the equation 2xy = 4 a linear equation? Explain why.This equation is not a linear equation because x and y are multiplied by each other.
9Writing an equation in Standard Form Ax + By = C y = 2/5x - 3(5)y = (2/5x - 3)55y = 2x - 155y -2x = 2x -2x – 1-2x + 5y = -15-1(-2x + 5y = -15)2x – 5y = 15A= 2, B= -5, and C = 15
10Writing an equation in Standard Form Ax + By = C Given A Point and a Slope Point (3,4) and m = 6y - y1 = m(x - x1) Use Point-Slope Formy - 4 = 6(x - 3) Substitute the valuesy - 4 = 6x – 18 Use Distributive Propertyy = 6x Add Liked Termsy = 6x – 14 Slope-Intercept Form-6x + y = 6x – 6x – 14 Move the x value-6x + y = -14 Add Liked Terms-1(-6x + y = -14) Multiply times -16x – y = 14 Standard Form
11Writing an equation in Standard Form Ax + By = C Given Two Points (6, -2) and (-4, 4) First: Find the Slope between the two pointsSecond: Use the Slope and the first point on the Point-Slope Form. Plug them in.
12Writing an equation in Standard Form Ax + By = C Given Two Points (6, -2) and (-4, 4) A = 3, B = 5 and C = 28
13• • Steps to Graph Equations in standard form Write the equation in standard formFind x-intercept, by letting y = 0, solve for x, plot the point where x crosses the x-axisFind y-intercept, by letting x = 0, solve for y, plot the point where y crosses the y-axisDraw a line through the 2 points.Graph 2 x + 3 y = 12Already using standard form: 2 x + 3y = 12Let y = 0 2 x + 3(0) = 122 x = 12x = 6x-intercept is at ( 6 , 0 )Let x = 0 2 (0) + 3 y = 123 y = 12y = 4y-intercept is at ( 0 , 4 )•( 0 , 4 )2 x + 3 y = 12•( 6 , 0 )13
14Your Turn! How do you graph a line which is in standard form? Graph 3x - 4y = -12x y3(3)0 - 4y = -12-43x - (4)0 = -12Graph the points and connect the dots
15Student ActivityYou will now receive a worksheet. Turn the worksheet in when completed.