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Linear Functions

Linear Functions. Review of Formulas. Formula for Slope. Standard Form. *where A>0 and A, B, C are integers. Slope-intercept Form. Point-Slope Form. Find the slope of a line through points (3, 4) and (-1, 6). Change into standard form . .

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Linear Functions

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  1. Linear Functions

  2. Review of Formulas Formula for Slope Standard Form *where A>0 and A, B, C are integers Slope-intercept Form Point-Slope Form

  3. Find the slope of a line through points (3, 4) and (-1, 6).

  4. Change into standard form.

  5. Change into slope-intercept form and identify the slope and y-intercept. M=2/3 and b=-3

  6. Write an equation for the line that passes through (-2, 5) and (1, 7): Find the slope: Use point-slope form: Change to slope-intercept form:

  7. x-intercepts and y-intercepts The intercept is the point(s) where the graph crosses the axis. To find an intercept, set the other variable equal to zero. (0, 3) is the y-intercept

  8. DO NOW: Find the intercepts and graph the line • 3x + 9y = -9 2) 4x – 2y = 16

  9. Horizontal Lines • Slope is zero. • Equation form is y = #. • Write an equation of a line and graph it with zero slope and y-intercept of -2. • y = -2 • Write an equation of a line and graph it that passes through (2, 4) and (-3, 4). • y = 4

  10. Vertical Lines • Slope is undefined. • Equation form is x = #. • Write an equation of a line and graph it with undefined slope and passes through (1, 0). • x = 1 • Write an equation of a line that passes through (3, 5) and (3, -2). • x = 3

  11. Graphing Lines *You need at least 2 points to graph a line. Using x and y intercepts: • Find the x and y intercepts • Plot the points • Draw your line

  12. Graph using x and y intercepts 2x – 3y = -12 x-intercept 2x = -12 x = -6 (-6, 0) y-intercept -3y = -12 y = 4 (0, 4)

  13. Graph using x and y intercepts 6x + 9y = 18 x-intercept 6x = 18 x = 3 (3, 0) y-intercept 9y = 18 y = 2 (0, 2)

  14. Graphing Lines Using slope-intercept form y = mx + b: • Change the equation to y = mx + b. • Plot the y-intercept. • Use the numerator of the slope to count the • corresponding number of spaces up/down. • Use the denominator of the slope to count the corresponding number of spaces left/right. • Draw your line.

  15. Slope m = -4 = -4 1 y-intercept (0, 1) Graph using slope-intercept form y = -4x + 1:

  16. Slope m = 3 4 y-intercept (0, -2) Graph using slope-intercept form 3x - 4y = 8 y = 3x - 2 4

  17. DO NOW: Write an equation that matches the graph. 1) 2)

  18. DO NOW: Write an equation that matches the graph. 1) 2)

  19. Parallel Lines • **Parallel lines have the same slopes. • Find the slope of the original line. • Use that slope to graph your new line and to write the equation of your new line.

  20. Graph a line parallel to the given line and through point (0, -1): Slope = 3 5

  21. Write the equation of a line parallel to 2x – 4y = 8 and containing (-1, 4): – 4y = - 2x + 8 y = 1x - 2 2 Slope = 1 2 y - 4 = 1(x + 1) 2

  22. Perpendicular Lines • **Perpendicular lines have the • opposite reciprocal slopes. • Find the slope of the original line. • Change the sign and invert the • numerator and denominator • of the slope. • Use that slope to graph your new • line and to write the equation • of your new line.

  23. Graph a line perpendicular to the given line and through point (1, 0): Slope =-3 4 Perpendicular Slope= 4 3

  24. Write the equation of a line perpendicular to y = -2x + 3and containing (3, 7): Original Slope= -2 Perpendicular Slope = 1 2 y - 7 = 1(x - 3) 2

  25. Write the equation of a line perpendicular to 3x – 4y = 8 and containing (-1, 4): -4y = -3x + 8 y - 4 = -4(x + 1) 3 Slope= 3 4 Perpendicular Slope = -4 3

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