find an equation of the line through these points

Question

Use the data points (28, 3.1) and (10, 2.2) to find an equation of the line through these points. Be sure to use the equation editor to show all steps (slope, point-slope form and slope intercept form).

Answer 1

 

slope = (3.1-2.2)/(28-10) = 0.9/ 18  

                                        = 9/180   <-- clearing the decimals by multiplying by 10/10

                                         = 1/20 = 0.05

 

Since y = mX+b then b = y - mX

 

  Substituting the second point (10,2.2) gives:    B = 2.2 - 10*0.05 = 2.2 - .5 = 1.7

 

  So the equation in slope intercept form is y = 0.05X + 1.7

 

   subtracting 2.2 from both sides:  y - 2.2 = .05X - 0.5

 

           factoring 0.05 out of the right side, the Point-slope form is (y-2.2) = 0.05( x - 10)

Answer 2

The shortcut to use the equation editor in Microsoft Word is  "alt" + "+=".  To clarity this, you press the alt key and the key that has the plus and equal sign at the same time.

 

The equation in following forms is as follows:

 

Point-slope form

           y - y₁ = m(x - x₁)

 

slope-intercept form         

      y = mx - mx₁ + y₁

 

where:

m is the slope between the two given points

(x₁ , y₁) is any of the given points