Determining Values

• 1). Isolate the variable for which you wish to solve. For example:
  
  2a + b + 3c = 5
  
  If you wish to solve for b, write:
  
  b = -2a - 3c + 5
  
  
• 2). Substitute values for the known variables. For example, if you know the values of a and c, insert them into the equation:
  
  a= 1
  c= -3
  
  b = -2(1) - 3(-3) + 5
  
  
• 3). Solve for the remaining variable. For example:
  
  b = -2(1) - 3(-3) + 5
  b = -2 + 9 + 5
  b = 12
  
  

Determining an Equation from Two Points

• 1). Subtract the two x-values of your points. For example, if the points are (1, 8) and (5, 0), perform 5 - 1 = 4.
  
  
• 2). Subtract the two y-values of your points. Make sure you do this in the same order you did for the corresponding x values. For example, if you subtracted 1 from 5, you must subtract 8 from 0 to arrive at -8.
  
  
• 3). Divide the difference in y-values by the difference in x-values. For example:
  
  -8 / 4 = - 2
  
  This is the slope of your line. Write this down in slope-intercept form ( y = mx + b, where m = the slope). For example, y = -2x + b.
  
  
• 4). Substitute one of the points into the slope-intercept equation. For example, 8 = -2(1) + b. Solve for b.
  
  8 = -2 + b
  b = 10
  
  This is your y-intercept. The equation for your line can be written y = mx + b, here y = -2x + 10.