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Graphing Linear Equations

Graphing Linear Equations. In Slope-Intercept Form. In order to graph using point plotting, you will need to create a table. You will need to choose at least 3 numbers for x and “plug” them into the equation to find corresponding y values. Plot the points. For Example: Graph y = 2x - 1.

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Graphing Linear Equations

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  1. Graphing Linear Equations In Slope-Intercept Form

  2. In order to graph using point plotting, you will need to create a table. You will need to choose at least 3 numbers for x and “plug” them into the equation to find corresponding y values. Plot the points For Example: Graph y = 2x - 1 x y Choose x values -1 2(-1)-1=-3 0 2(0)-1 = -1 1 2(1)-1 = 1 “plug” x into the equation

  3. Graph using point plotting x y (-2) + 3 = 2 -2 0 2 (0) + 3 = 3 (2) + 3 = 4

  4. These equations are all in Slope-Intercept Form: Notice that these equations are all solved for y.

  5. Just by looking at an equation in this form, we can draw the line (no tables). • The constant is the y-intercept. • The coefficient is the slope. Constant = 1, y-intercept = 1. Coefficient = 2, slope = 2. Constant = -4, y-intercept = -4. Coefficient = -1, slope = -1. Constant = -2, y-intercept = -2. Coefficient = 3/2, slope = 3/2.

  6. The formula for Slope-Intercept Form is: • ‘b’ is the y-intercept. • ‘m’ is the slope. On the next three slides we will graph the three equations: using their y-intercepts and slopes.

  7. right 1 up 2 right 1 up 2 1) Plot the y-intercept as a point on the y-axis. The constant, b = 1, so the y-intercept = 1. 2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = 2, so the slope = 2/1.

  8. down 1 down 1 right 1 right 1 1) Plot the y-intercept as a point on the y-axis. The constant, b = -4, so the y-intercept = -4. 2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = -1, so the slope = -1/1.

  9. right 2 up 3 right 2 up 3 1) Plot the y-intercept as a point on the y-axis. The constant, b = -2, so the y-intercept = -2. 2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = 3/2, so the slope = 3/2.

  10. Sometimes we must solve the equation for y before we can graph it. The constant, b = 3 is the y-intercept. The coefficient, m = -2 is the slope.

  11. down 2 down 2 right 1 right 1 1) Plot the y-intercept as a point on the y-axis. The constant, b = 3, so the y-intercept = 3. 2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = -2, so the slope = -2/1.

  12. Important!!! This is one of the big concepts in Algebra. You need to thoroughly understand this! Slope – Intercept Form y = mx + b m represents the slope b represents the y-intercept

  13. Graphing Using the Slope-Intercept Form

  14. To graph a linear equation, you will need to find the slope and the y-intercept for the equation. Remember: y = mx + b slope Y-intercept (the point where the graph crosses the y-axis)

  15. Slope = Y-intercept = Graph 1. Plot the y-intercept • Use the slope to find • the next point • Slope = “rise over run”

  16. Graph 2x + 5y = 10 using the slope-intercept form: (put the equation in slope-intercept form first) 2x + 5y = 10 5y = 10 – 2x y = 2 – 2/5 x slope = -2/5 y – intercept = 2 A negative slope means you will go down then right from the y-intercept

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