If a line is passing through the points (-8,7) and (-3,1) with an X-intercept of 6...How do you solve that?

Question

I am unsure what to do here. My Calculus teacher is doing this new thing where he doesn't teach but instead has the class figure it out. How can we figure anything out if we are all lost? Please help!!

Answer 1

The slope of the line is (1-7)/(-3-(-8)) = -6/5

 

If the x-intercept is 6, then the point (6,0) is also on the line.

 

So, using the points (-3,1) and (6,0), the slope would have to be -6/5 as well.  However, using the points (-3,1) and (6,0), the slope is -1/9.  

 

Thus, it is not possible for a line containing the points (-8,7) and (-3,1) to have an x-intercept of 6.

 

The idea here is that, the slope of a line is always the same regardless of which two points on the line are used to determine the line's slope.

 

Perhaps your instructor was asking if it was possible for the line to have x-intercept 6 given that (-8,7) and (-3,1) were points on the line?