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### W200

1. 1. Solving & Graphing Simple Linear Equations Click on Picture to move to next slide By: Elizabeth Eme
2. 2. A linear equation is a first degree polynomial equation 1. Slope-intercept form – Formula & definition – Example – Pop Quiz 2. General form – Formula & definition – Example – Pop Quiz 3. Graphing – Using T-chart – Using Slope & y-intercept – Pop Quiz 2
3. 3. Slope – Intercept Form • y = mx + b [m=slope; b= y-intercept] • Slope – Intercept form is one way to express a linear equation. Equations may begin in slope-intercept form or they may be solved into slope-intercept form. • This form allows a student to read the slope and y-intercept directly from the equation. • Slope is the rate of change between points. The y-intercept is where the line crosses the y-axis. Next 3
4. 4. Slope - Intercept Form • Original Equation y + 4 = -7 (x – 1) • Distribute -7 to (x-1) y + 4 = -7*x -7*(-1) y + 4 = -7x + 7 • Subtract 4 from both sides y +4 – 4 = -7x + 7 – 4 y = -7x + 3 • Slope = -7; y-intercept = 3 Next 4
5. 5. Slope – Intercept Form • Pop Quiz! – What does the ‘m’ stand for in a linear equation in the form y = mx + b? • A) x-intercept • B) y-intercept • C) slope (answers will be given at the conclusion) Main Menu 5
6. 6. General/Standard Form • ax + by = c • General or standard form is another way to express a linear equation. The equation may begin in this form or be solved into this form. • The slope may be determined from this form by taking the opposite sign of a÷b (i.e. –a÷b) • The y-intercept may be determined by taking c÷b Next 6
7. 7. General/Standard Form • Original Equation 2 (5 + 3y) = - (x – 4) • Distribute -2 to (5 + 3y) on the left side and -1 to (x - 4) on the right side. 2*5 + 2*3y = -1*x – 1*(-4) 10 + 6y = -x +4 • Subtract 10 from both sides 10 – 10 + 6y = -x + 4 – 10 6y = -x – 6 • Add x to both sides + x + 6y = - x + x – 6 x + 6y = -6 • Slope = (-1÷6)=-1/6; y-intercept = (-6)÷6= -1 Next 7
8. 8. General/Standard Form • Pop Quiz! – General/Standard form of a linear equation is: • A) y = mx + b • B) ax + by = c • C) y -y1 = m(x – x1) (answers will be given at the conclusion) Main Menu 8
9. 9. Graphing Linear Equations • Using T- Chart: – Pick any x-values [ I choose {-2, -1, 0, 1, 2} ] and plug them into the linear equation to get a y-value. • Given: y = 5x + 8 x= -2; y = 5(-2) + 8 .. y = -10 + 8 .. y = -2 x= -1; y = 5(-1) + 8 .. y = -5 + 8 .. y = 3 x= 0; y = 5(0) + 8 .. y = 0 + 8 .. y = 8 x= 1; y = 5(1) + 8 .. y = 5 + 8 .. y = 13 x= 2; y = 5(2) + 8 .. y = 10 + 8 .. y = 18 • From there, you will plot each point (-2, -2), (-1, 3), (0, 8), (1, 13), (2, 18) and connect the dots with a straight line placing arrows on each end of the line indicating the line will continue both ways. Next
10. 10. Graphing Linear Equations • Using slope & y-intercept – When a linear equation is in slope intercept form, plot the y- intercept and use the slope to guide you to other points. • Given: y = ½x + 3 • If you start on the y-axis at the point (0, 3), use the slope to guide you up 1 and to the right 2 to the point (2, 4). The next point would be ( 4, 5). Then go back to • the point (0,3) and plot a point • down 1 and to the left 2 to (-2, -2). The next point would be (-4, 1). You would then connect these dots with arrows on each end indicating the line continues. Next
11. 11. Graphing Linear Equations • Pop Quiz! – One way to graph a linear equation is to use the slope of the equation and y- intercept, starting at the y-intercept and using the slope to guide you. • True • False (answers will be given at the conclusion) Next 11
12. 12. Conclusion • There are many types of linear equations with multiple ways to solve and graph each equation. • Two types of linear equations are slope-intercept and general form. • Two ways to graph linear equations are using a t- chart and using the y-intercept and guiding the next points with the slope. • To watch a video about solving linear equations please, visit http://patrickjmt.com/solving-linear-equations/ Pop quiz answers: 1) C 2) B 3) True Main Menu 12