Gold Day – 2/24/2015 Blue Day – 2/25/2015.  Unit 5 – Linear functions and Applications  Review – slope, slope intercept form  Standard Form  Finding.

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Presentation transcript:

Gold Day – 2/24/2015 Blue Day – 2/25/2015

 Unit 5 – Linear functions and Applications  Review – slope, slope intercept form  Standard Form  Finding equations of a line using the intercepts

 Slope-intercept form is the equation of a line. Dependent variable It is also our y-coordinate Independent variable It is also our x-coordinate Slope Rate of change Rise over run y-intercept Where the line we are graphing crosses the y-axis Slope intercept form is just one form of a linear equation. Another form is Standard Form.

 The standard form of a linear equations is Ax+By=C, where A, B, and C are real numbers, and A and B are not both zero.  Standard form is perfect for finding the intercepts of a linear equation.

y x (x, 0)(x, 0) Standard form of a linear equation is Ax + By = C. A and B are not both zero. A quick way to graph this form is to plot its intercepts (when they exist). Draw a line through the two points. Ax + By = C The x -intercept is the x -coordinate of the point where the line intersects the x -axis. The Y -intercept is the Y -coordinate of the point where the line intersects the x -axis. Ax + By = C (0, y)(0, y)

 x-intercept  The point where the graph crosses the x-axis.  x-intercepts happen when the y-coordinate is zero.  To find the x-intercept from an equation, replace y with 0 and solve for x.

 y-intercept  The point where the graph crosses the y-axis.  y-intercepts happen when the x-coordinate is zero.  To find the y-intercept from an equation, replace x with 0 and solve for y.

 Find the x- and y-intercepts of 3x+4y=8. Step 1 To find the x- intercept, substitute 0 for y and solve for x. 3x + 4y = 8 3x + 4(0) = 8 3x = 8 Step 2 To find the y- intercept, substitute 0 for x and solve for y. 3x + 4y = 8 3(0) + 4y= 8 4y = 8 y = 2 Yes! This is a one step equation.

 Find the x- and y-intercepts of 4x–9y=-12. Step 1 To find the x- intercept, substitute 0 for y and solve for x. 4x - 9y = -12 4x - 9(0) = -12 4x = -12 x = -3 Step 2 To find the y- intercept, substitute 0 for x and solve for y. 4x - 9y = -12 4(0) - 9y= y = -12 x = -3

The equation of a vertical line cannot be written in slope- intercept form because the slope of a vertical line is not defined. Every linear equation, however, can be written in standard form— even the equation of a vertical line. HORIZONTAL AND VERTICAL LINES HORIZONTAL LINES The graph of y = c is a horizontal line through (0, c ). VERTICAL LINES The graph of x = c is a vertical line through ( c, 0).

Graph y = 3 and x = –2 S OLUTION The graph of y = 3 is a horizontal line that passes through the point (0, 3). Notice that every point on the line has a y-coordinate of 3. (0, 3) The graph of x = –2 is a vertical line that passes through the point (– 2, 0). Notice that every point on the line has an x-coordinate of –2. (–2, 0) y = 3 x = –2

 Graph of 4x–9y=-12 using intercepts x = -3 x-intercept y-intercept

 Split off

 Change Ax + By=C to y=mx + b Ex: 1. -3x + 4y = 82. 6x + 3y = 27