2. Aim: Slope/Intercept Form of Equation Course: Applied Geometry Do Now: Graph the following equations on the same set of coordinate axes: Aim: What can we learn about a linear equation when in the form y = mx + b? y = 2x y – 2x = 3 2x = 5 + y y = 2x 1. Solve for y y = 2x + 3 y = 2x – 5

3. Aim: Slope/Intercept Form of Equation Course: Applied Geometry Do Now x y 123456789 -2-3-4-5-6 1 2 3 4 5 6 7 8 9 -2 -3 -4 -5 -6 -7 -8 -9 xyy = 2x 0 1 2 0 2 4 2(0) 2(1) 2(2) xy2x + 3 0 1 2 3 5 7 2(0) + 3 2(1) + 3 2(2) + 3 xy2x - 5 0 1 2 -5 -3 2(0) - 5 2(1) - 5 2(2) - 5 2. Create Tables of Values 3. Plot Points 4. Label Lines y = 2 x y = 2 x - 5 y = 2 x + 3

4. Aim: Slope/Intercept Form of Equation Course: Applied Geometry Slope of Equation y 1 2 3 4 5 6 7 8 9 What conclusions can you make about these linear equations? They look parallel. y = 2x y = 2x + 3 y = 2x - 5 When an equation is in the form of y = mx + b the coefficient, m, of x is the slope of the line. They have the same slope: +2 are y = 2x y = 2x - 5 y = 2x + 3

5. Aim: Slope/Intercept Form of Equation Course: Applied Geometry The y-intercept x y 1 3 slope y = 2x (0,3) (0,0) (0,-5) y = 2x y = 2x - 5 y = 2x + 3 y- intercept + 0 y = 2x + 3 y = 2x - 5 Slope Intercept Form of a Linear Equation y = mx + b slopey-intercept Equation: y = 2x - 1 slope = 2/1 = 2 y-intercept = -1 What else can we conclude? y-intercepts

6. Aim: Slope/Intercept Form of Equation Course: Applied Geometry Model Problem Find the slope and the y-intercept of the line that is the graph of the equation 4x + 2y = 10. 1. Change to slope/intercept form 4x + 2y = 10 -4x 2y = 10 - 4x 2y = -4x + 10 22 y = -2x + 5 slope -2 y-intercept + 5 2. Equation: y = mx + b slope = m y-intercept = b

7. Aim: Slope/Intercept Form of Equation Course: Applied Geometry Model Problem Write an equation of a line whose slope is 1/2 and whose y-intercept is -4 Equation: y = mx + b slope = m = 1/2 y-intercept = b = -4 y = 1/2x - 4 Graph a line whose slope is -2/3 and whose y-intercept is + 3. y-intercept is + 3 (0, 3) +3-run y = -2/3 x + 3 -2 -rise

8. Aim: Slope/Intercept Form of Equation Course: Applied Geometry Slope-Intercept Form of Linear Equation If the equation of a line is written in the form y = mx + b, then the slope of the line is m and the y-intercept is b. Logic-conditional If the slope of the line is m and the y-intercept is b, then the equation of a line is y = mx + b Logic-converse Two lines are parallel if and only if their slopes are equal. Logic-biconditional

9. Aim: Slope/Intercept Form of Equation Course: Applied Geometry What is the slope? the y-intercept? Model Problem Graph the following linear equations: Slope Intercept Form of a Linear Equation y = mx + b slopey-intercept Slope Intercept Form of a Linear Equation y = mx + b slopey-intercept

10. Aim: Slope/Intercept Form of Equation Course: Applied Geometry Model Problem Graph the line that is parallel to and passes through (-2, -3)

11. Aim: Slope/Intercept Form of Equation Course: Applied Geometry Model Problem Graph the line that is parallel to and passes through (-3, 2)