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Graphing linear equations

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Graphing linear equations

  1. 1. Graphing Linear Equations<br />
  2. 2. Linear Equations are most often expressed in one of three forms:<br />Slope-Intercept Form: 𝑦=π‘šπ‘₯+𝑏,<br />Point-Slope Form: π‘¦βˆ’π‘¦1=π‘š(π‘₯βˆ’π‘₯1), and<br />Standard Form: 𝐴π‘₯+𝐡𝑦=𝐢.<br />Each form allows for quick and easy ways to graph the line they represent.<br />Β <br />Forms of Linear Equations<br />
  3. 3. One method for graphing a line is to use a table. This is most useful when we have an equation in slope-intercept form (𝑦=π‘šπ‘₯+𝑏).<br />The steps are:<br />Assign a value to the x-variable,<br />Calculate the corresponding value for the y-coordinate, and<br />Repeat.<br />In this way, we can create a table of ordered pairs and plot them on the coordinate plane.<br />Β <br />Make a Table<br />
  4. 4. Consider the equation 𝑦=12π‘₯+2. <br />Β <br />Make a Table<br />𝑦=12(βˆ’πŸ)+2<br />Β <br />(-2,1)<br />=1<br />𝑦=12(𝟎)+2<br />Β <br />=2<br />(0, 2)<br />𝑦=12(𝟐)+2<br />Β <br />(2, 3)<br />=3<br />
  5. 5. Another method for graphing lines when an equation is in slope-intercept form is as follows:<br />Plot the y-intercept on the coordinate plane; that's the point (0, b).<br />Use the slope to find another point (and repeat).<br />Draw a line through the points.<br />Use the slope and intercept<br />
  6. 6. Consider the equation𝑦=βˆ’54π‘₯+7.<br />Β <br />Plot the y-intercept <br />Use the slope to find another point (and repeat).<br />Draw a line through the points.<br />Use the slope and intercept<br />(0, b) = (0, 7)<br />From the intercept, move down 5 and right 4 (or up 5 and left 4).<br />
  7. 7. This method is very similar to the slope-intercept method. To graph a line using this method, do the following:<br />Plot the point (π‘₯1, 𝑦1).<br />Use the slope to find another point (and repeat).<br />Draw a line through the points.<br />Β <br />Use a point and the slope<br />
  8. 8. Consider the equationπ‘¦βˆ’2=73(π‘₯+3).<br />Β <br />Plot the point (π‘₯1, 𝑦1)<br />Use the slope to find another point (and repeat).<br />Draw a line through the points.<br />Β <br />Use a point and the slope<br />(π‘₯1, 𝑦1)= (-3, 2)<br />Β <br />From (-3, 2), move up 7 and right 3 -– or down 7 and left 3.<br />
  9. 9. This method is used when the line is in Standard Form (𝐴π‘₯+𝐡𝑦=𝐢). <br />The x-intercept is easily calculated by setting y to 0 and solving for π‘₯.<br />The y-intercept is calculated by setting π‘₯ to zero and solving for 𝑦.<br />Plot the two intercepts and draw a line through them.<br />Β <br />Use the Intercepts<br />
  10. 10. Consider the equation3π‘₯βˆ’5𝑦=βˆ’15.<br />Β <br />Set 𝑦=0 and solve for π‘₯.<br />Set π‘₯=0 and solve for 𝑦.<br />Draw a line through the points.<br />Β <br />Use the Intercepts<br />3π‘₯=βˆ’15; π‘₯=βˆ’5(βˆ’5,Β 0)<br />Β <br />βˆ’5π‘₯=βˆ’15; 𝑦=3(0,Β Β 3)<br />Β <br />

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