Chapter 1.1, Problem 23E

To determine

Find the three additional points through which the line passes by the given point and the given slope.

Answer to Problem 23E

The points through which line passes may be $(1,2),(2,2.5),(3,3)$ and so on.

Explanation of Solution

Given:

It is given in the question that the coordinate and slope are $(7,-2)$ and $m=\frac{1}{2}$ .

Concept Used:

In this, use the concept that in term of plot a slope we also use the term rise/run,which means Rise means up and down,thinking of the sun rising if the number is positive and the sun is setting then the number is negative ,Similarly Run means left and right if it is is right then the number is positive and to the left if the number id negative.

Calculation: Now by taking the concept in mind,we now start with the point $(7,-2)$ ,

  

Now ,the slope is already a fraction,so no need to change it: $m=\frac{1}{2}=\frac{rise}{run}$

Now,starting at point $(7,-2)$ ,count up $1$ (because of the $+1$ in numerator of slope),and count to the right $2$ (because of the $+2$ in the denominator).This new point is $(7+2,-2+1)=(9,-1)$ .

  

Now go through this process $2$ more times,(up $1$ ,right $2$ ),in order to find a total of $3$ points.

  

Conclusion:

The points may be $(1,2),(2,2.5),(3,3)$ .