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Understanding Slope: Positive, Negative, and Zero in Linear Equations

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This overview explores the concept of slope in linear equations, detailing how to identify positive, negative, zero, and undefined slopes. It emphasizes the importance of the slope-intercept form (y = mx + b), where (m) represents the slope and (b) the y-intercept. The guide discusses how to convert linear equations into slope-intercept form using inverse operations, allowing for effective graphing on a coordinate plane. Mastery of these concepts is essential for solving equations and visualizing relationships between variables.

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Understanding Slope: Positive, Negative, and Zero in Linear Equations

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Presentation Transcript

  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 SOLVING FOR Y AND PUTTING EQUATIONS INTO Slope - Intercept Form

  3. Any linear equation can be graphed on a coordinate plane. • In order to be able to graph the equation, it has to be set up properly. • Doctor / surgery • Driving • Vacation • The ONLY way to graph an equation is from slope-intercept form. CONCEPT:

  4. y = mx + b Slope y-intercept **Slope-intercept form: y= mx+ b mis the slope and bis the y-intercept. m and b are place holders for numbers. In slope-int. form, m & b will be numbers

  5. y = 6x + 2 y = x - 5

  6. 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.

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

  8. Let’s put this equation in slope-intercept form: 5y = 3x

  9. 2x + 3y = -12

  10. 3y = 4x + 15

  11. You must always have 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

  12. Change to slope-intercept form: 4x + 3y = 9

  13. -5x – 9x = 4y – 4 -6y – 2x = 8 7y – 7x = -4 1y – 3x = 4

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