what equation describes the line that passes through (2, 1) and (0, -5)?

Question

y = 1/3x - 5

 

 

y = 3x - 5


y = -1/3x - 5


y = - 3x - 5

Answer 1

Given a multiple choice question (with exactly one correct answer), you may either (1) solve the problem, then select the correct answer, or (2) eliminate possible answers without solving the entire problem.

 

Let's try number (2).

 

You should notice immediately that the y-intercept (the value of y when x=0) is given as the point (0,-5).  In slope-intercept form (y=mx+b) that means that b, the y-intercept, is -5.  The equation for the line must look like:

  y = mx -5

 

Now, the people who wrote the distractors (possible answers) knew this process, so they very wisely put (-5) in every choice.

 

What's left;  just the slope.

 

The slope is often called "rise over run" because it is the increase in the y value divided by the increase in the x value.

     m = (y₂ - y₁) / (x₂ - x₁)

 

For this problem:

   m = ( (-5) - 1 ) / ( 0 - 2 )

   m = -6/-2

   m = 3

 

The formula for the line is:    y=3x-5  

 

So, we had to solve the problem anyway.  But, let's put the points in increasing x order:   (0,-5) and (2,1)

Now, think about a graph going from -5 to +1 (rise) and from 0 to 2 (run) and get 6/2 = 3 (rise over run) for the slope.