Presentation on theme: "Rectangular Coordinate System"— Presentation transcript:
1 Rectangular Coordinate System X-axisY-axis(0,0)OriginQuadrant IIQuadrant IQuadrant IIIQuadrant IV
2 Rectangular Coordinate System X-axisY-axis(0,0)Rectangular Coordinate System(0,5)(-5,4)(1,3)(6, -3)(-2,-4)
3 Linear Equations in Two Variable A linear equation in two variables is an equation of the formAx + By = Cwhere A, B, C are real numbers and A & B are both not zeroExamples of linear equation in two variables :3x + 4y =23X=67z + 4y =16X + 9y = 0The graph of any linear equation in two variables is a straight line
4 Solutions of Linear Equations in Two Variables Example:2x + y = 3Some SolutionsExample:y = 3x - 1Some Solutionsx yx y3-111122-125-15-1- 4
5 Graphing Linear Equations in Two Variables 54321-2-3-4-5yxGraph:2x + y = 3(0, 3)31-1x y25(1, 1)(2, -1)
6 Graphing Linear Equations in Two Variables The graph of 2x + y = 3 is a line.The solution set of a linear equation in two variables is all the points that lie on the line of its graph54321-2-3-4-5yx
7 X-intercepts and Y-intercepts The x-intercept is the point where the line intersects the x-axisWhat is the y-coordinate of the x-intercept?The y-intercept is the point where the line intersects the y-axisWhat is the x-coordinate of the y-intercept?54321-2-3-4-5yx2x + y = 3
8 Y - Intercepts The y – intercept is the y – value when x = 0. When using a graph, the y – intercept is where the graph crosses the y – axis.The y – intercept of the line to the right is …To find the y-intercept, let x=0 in the given equation and solve for y. Then (0,y) is the y-intercept.
9 X - Intercepts The x – intercept is the x – value when y = 0. When using a graph, the x – intercept is where the graph crosses the x – axis.x – intercept is 2.The x – intercept of the line to the right is …To find the x-intercept, let y=0 in the given equation and solve for x. Then (x,0) is the x-intercept
10 y x Special Cases Graph: y = 3 This is the set of points that have a y-coordinate of 3.(x, 3) for all x.54321-2-3-4-5yxThe Graph of y= 3 is a horizontal line
11 y x Special Cases Graph: x = 5 This is the set of points that have a x-coordinate of 5.(5, y) for all y.54321-2-3-4-5yxThe graph of x= 5 is a vertical line
12 Graphing ax + by = c What about 3x + 4y = –12 ? Step 1: Put equation in slope – intercept formThis means solve for y.Step 2: Plot the y – intercept.Step 3: Starting at the y – intercept, use the slope to find other points.A slope of meansDown 3, Right 4…or…Up 3, Left 4 (the 3 or 4 can be negative, but not both).