Presentation on theme: "Section 3-5 Lines in the Coordinate Plane SPI 21C: apply concept of rate of change to solve real-world problems SPI 21D:"— Presentation transcript:
1 Section 3-5 Lines in the Coordinate Plane SPI 21C: apply concept of rate of change to solve real-world problems SPI 21D: determine the slope given a graph of a linear equations (VS) SPI 21E: determine the slope when given the coordinates of 2 pointsObjectives:Graph lines given their equationsWrite equations of linesLinear Equation:equation of a lineall points on the line are a solution to the equationForms of Linear Equations:Slope-InterceptStandard FormPoint-slope Form
2 Review Slope Formula Slope or Rate of Change Slope = change in ychange in xSlope = y2 – y1x2 – x1One pair ofcoordinatesThe other pairof coordinatesUsing Slope to graph an equationFrom known point:Top number is rise: Move up (+) or down (-)Bottom number: Move right
3 Review Slope Intercept Form y = mx + bYIIIIIIIVf(x)slopey-interceptGraph y = 3 x + 24X1. Plot y-intercept2. From known point, plotslope. (Rise over run)3. Connect the 2 pointswith a line.
4 Practice II I III IV Slope Intercept Form Graph y = - 1 x – 2 2 1. Plot y-interceptX2. From known point, plotslope.3. Connect the 2 pointswith a line.
5 Review: Standard Form of a Linear Equation (Graph using x and y intercepts) Ax + By = CGraph 6x + 3y = 12Y1. Find x intercept:Substitute 0 for y; solve for xIIIIIIIV6x + 3(0) = 126x = 12x = 2(0, 4)(2, 0)X2. Find y intercept:Substitute 0 for x; solve for y6(0) + 3y = 123y = 12y = 43. Plot x and y intercepts: (2, 0) and (0, 4)Connect points with line
6 PracticeGraph a Linear Equation in Standard Form (Graph using x and y intercepts)Ax + By = CGraph -2x + 4y = - 8Y1. Find x intercept:Substitute 0 for y; solve for xIIIIIIIV-2x + 4(0) = - 8-2x = - 8x = 4(4, 0)X(0, -2)2. Find y intercept:Substitute 0 for x; solve for y-2(0) + 4y = - 84y = - 8y = - 23. Plot x and y intercepts: (4, 0) and (0, -2)Connect points with line
7 Alternate Method to Graph Equation in Standard Form Change Equation to Slope-Intercept Form Ax + By = Cy = mx + bGraph -2x + 4y = - 8YIIIIIIIV1. Use Properties of Equality toSolve equation in terms of y.-2x + 4y = - 8+2x = x4y = 2x – 8y = 1 x – 22(2, -1)X(0, -2)2. Plot the y-intercept: -2Plot the slope: ½3. Plot x and y intercepts: (4, 0) and (0, 3)Connect points with line
8 Change Standard Form to Slope- Intercept Form and Graph PracticeChange Standard Form to Slope- Intercept Form and GraphGraph 6x + 3y = 12Y1. Use properties of equality tosolve the equation in terms of y.IIIIIIIV6x + 3y = 12-6x = 12 – 6x3y = -6x + 12y = -2x + 4(0, 4)(1, 2)X2. Plot the y-intercept: 4Plot the slope: - 2
9 Review: Point-slope Form of a Linear Equation Write an equation of a line given two points. A(-2, 3) and B(1, -1).y – y1 = m(x – x1)(x, y)(x1, y1)1. Find the slope.2 Set of coordinatesm = y2 – y1 = 3 – (-1) = 4x2 – x (-2) –Write an equation of the line thru point P(-1, 4) with slope 3.Substitute known values into the equation.2. Select one of the points and substitute values into equation. Pick (-2, 3).y – (4) = 3 (x – (-1)) Sub.y – 4 = 3 (x + 1) Simplifyy – y1 = m(x – x1)y – y1 = m(x – x1)y = - 4/3(x – (-2))y – 3 = - 4/3(x + 2)
10 II I III IV Equations of Horizontal and Vertical Lines Graph a Horizontal Linear EquationYGraph the equation y = 3.IIIIIIIV1. Plot the point (0, 3)2. Draw a horizontal line.(0, 3)XFor all values of x in the graph of y = 3, what is the value of y?
11 Practice II I III IV Equations of Horizontal and Vertical Lines Graph a Vertical Linear EquationYGraph the equation x = 4.IIIIIIIV1. Plot the point (4, 0)2. Draw a vertical line.(4, 0)XFor all values of y in the graph of x = 4, what is the value of x?