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Solving Systems By Graphing

Solving Systems By Graphing. y = mx + b m = slope b = y-intercept. Slope-Intercept form for the equation of a line Slope = rise run y-intercept is the point where the line crosses the y-axis. Slope-Intercept Form. Graph: y = ½ x + 3. 1 st : graph the y-intercept (the b).

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Solving Systems By Graphing

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  1. Solving Systems By Graphing

  2. y = mx + b m = slope b = y-intercept Slope-Intercept form for the equation of a line Slope = rise run y-intercept is the point where the line crosses the y-axis Slope-Intercept Form

  3. Graph: y = ½ x + 3 1st: graph the y-intercept (the b) 2nd: follow the slope (rise over run) 3rd: connect the dots We’re graphing lines, so don’t forget to draw a line!

  4. Ax + By = C Ax = C +By = C Standard form for the equation of a line Finds the x-intercept Finds the y-intercept Standard Form

  5. Definition of an Intercept • An intercept is the point where a line crosses either of the axes. • When the line crosses the y-axis, it is called the y-intercept • When the line crosses the x-axis, it is called the x-intercept • The coordinates for a y-intercept comes in the form (0,y) • The coordinates for an x-intercept comes in the form (x, 0)

  6. Graphing Standard Form Graph: 3x – 4y = 24 3x – 4(0) = 24 3x = 24 3 3 x = 8 • 1st find the x-int • Set y = 0 • Solve for x

  7. Graphing Standard Form 3(0) – 4y = 24 -4y = 24 -4 -4 y = -6 • Now solve for y • Set x = 0 • Now graph the intercepts with those values that we found

  8. Graph: 3x – 4y = 24 1st: graph the x-intercept: 8 2nd: graph the y-intercept: -6 3rd: connect the dots We’re graphing lines, so don’t forget to draw a line!

  9. Solving Systems of Equations • A system of equations is 2 or more equations using the same 2 or more variables • Can be solved 3 ways • By graphing • By substitution • By elimination • We will focus on the graphing part now • The solution to a system is the set of all points both lines have in common

  10. Solving Systems of Equations • There are 3 possibilities when solving a system of equations. • There can be 1 solution (intersecting lines) • There can be no solution (parallel lines) • There can be infinitely many solutions (same line) • Let’s see an example of each

  11. Solve: y = ½ x + 3 y = 4x - 4 1st: graph the 1st equation 2nd: graph the 2nd equation 3rd: the solution is the point of intersection Our Solution is (2,4)

  12. Solve: y = 2x + 3 y = 2x – 1 1st: graph the 1st equation 2nd: graph the 2nd equation 3rd: These are parallel lines There is no solution

  13. Solve: y = ¾ x – 2 y = ¾ x – 2 1st: graph the 1st equation 2nd: graph the 2nd equation 3rd: These are the same line There are infinitely many solutions

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