Chapter 3.3, Problem 50HP

To determine

To Find: The value of ‘d’ for which the slope of the line passing through points $\left(a,b\right)\&\left(c,d\right)$ is $\frac{1}{2}.$

Answer to Problem 50HP

  $d=\frac{c-a+2b}{2}$

Explanation of Solution

Given information:

Line passing through $\left(a,b\right)\&\left(c,d\right)$

Concept and Formula Used:

Slope of line passing through two points is given by $m=\left(\frac{y_2-y_1}{x_2-x_1}\right)$ .

Calculation:

It is given that line passing through $\left(a,b\right)\&\left(c,d\right)$ .

Slope of line is given by

  $\begin{array}{l}m=\left(\frac{y_2-y_1}{x_2-x_1}\right)\\ \text{where }\left(x_1,y_1\right)=\left(a,b\right),\left(x_2,y_2\right)=\left(c,d\right)\&m=\frac{1}{2}\\ \frac{1}{2}=\left(\frac{d-b}{c-a}\right)\\ \text{Cross multiply}\\ 1\left(c-a\right)=2\left(d-b\right)\\ \frac{c-a}{2}=d-b\\ \frac{c-a}{2}+b=d\\ d=\frac{c-a+2b}{2}\end{array}$

Conclusion:

  $d=\frac{c-a+2b}{2}$