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Quick Review:

Slope is… Steepness of a line , m , rise , change in y , common difference run change in x Positive Slope: Negative Slope: Zero Slope: Undefined Slope:. Quick Review:. Chapter 12-3. Slope and Intercepts.

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Quick Review:

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  1. Slope is… Steepness of a line, m, rise, change in y, common difference runchange in x Positive Slope: Negative Slope: Zero Slope: Undefined Slope: Quick Review:

  2. Chapter 12-3 Slope and Intercepts

  3. How to graph a linear equation (one that forms a straight line and also has a common difference – constant slope) using intercepts. What slope-intercept form is and how to put any linear equation into slope-intercept form. Topics to learn today:

  4. There are 2 different ways to graph a linear equation: • Finding the x and y intercepts and plotting them on a graph (today). • Using the slope and y-intercept (in slope-intercept form) to graph 2 points on a coordinate plane (Wednesday).

  5. Steps to graph a linear equation using intercepts: Find the x-intercept (y=0) Find the y-intercept (x=0) Plot the points Connect the points with a line

  6. **The x-intercept of a line is the value of x where the line crosses the x-axis (where y = 0). x-axis y-axis X-intercept:

  7. **The y-intercept of a line is the value of y where the line crosses the y-axis (where x = 0). x-axis y-axis y-intercept:

  8. 8x = 24 8 8 Graphing linear equations: Graph the line 8x – 6y = 24 using the intercepts. 1. Find the x-intercept (y = 0). 8x – 6y = 24 8x – 6(0) = 24 8x = 24 The ordered pair for the x-intercept is (3,0). x = 3 The x-intercept is 3.

  9. –6y –6 = 24 –6 Graphing linear equations: 2. Find the y-intercept (x = 0). 8x – 6y = 24 8(0) – 6y = 24 –6y = 24 y = –4 The ordered pair for the y-intercept is (0,-4). The y-intercept is –4.

  10. The graph of 8x – 6y = 24 is the line that crosses the x-axis at the point (3, 0) and the y-axis at the point (0, –4).

  11. y = mx + b Slope y-intercept **Slope-intercept form: y= mx+ b mis the slope and bis the y-intercept.

  12. Slope-intercept form is how you need an equation to be so that you can EASILY graph it. Standard form is another way of seeing a linear equation, but you can’t graph it – you would have to put it into slope-intercept form.

  13. Helpful Hint The form Ax + By = C is called the Standard Formof a Linear Equation. **Remember… slope-intercept form is y= mx+ b

  14. To put any linear equation into slope-intercept form, you have to use inverse operations to solve for y.

  15. Let’s put this equation in slope-intercept form: 5y = x 5 3 3 5 5 y = x + 0 3 m = 5 3 The slope of the line 5y = 3x is , and the y-intercept is 0. 5 5y = 3x 5y = 3x Divide both sides by 5 to solve for y. The equation is in slope-intercept form. b = 0

  16. You always have to have a y, m, x, and b. This means that if an equation says y=mx, you assume that b is 0 (and add 0). y = mx + 0

  17. 3y 3 4 –4x 3 3 4 9 3 = + 3 4 y =- x + 3 m =- 3 The slope of the line 4x+ 3y = 9 is – , and the y-intercept is 3. Change from standard form to slope-intercept form: 4x + 3y = 9 4x + 3y = 9 –4x–4x Subtract 4x from both sides. 3y = 9 – 4x Rewrite to match slope-intercept form. 3y = –4x + 9 Divide both sides by 3. The equation is in slope-intercept form. b= 3

  18. -5x – 9x = 4y – 4 -6y – 2x = 8 7y – 7x = -4 1y – 3x = 4

  19. A video club charges $8 to join, and $1.25 for each DVD that is rented. The linear equation y = 1.25x + 8 represents the amount of money y spent after renting x DVDs. Graph the equation by first identifying the slope and y-intercept. The equation is in slope-intercept form. y = 1.25x + 8 m =1.25 b = 8

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