Chapter 1, Problem 10RE

a.

To determine

To find : the equation of the line.

Answer to Problem 10RE

the equation of line is $y=-\frac{3}{2}x+\frac{1}{2}$.

Explanation of Solution

Given information :

Point is $\left(-3,5\right)$.

Slope of the line is $m=-\frac{3}{2}$.

Formula used :

The equation of line is $y=mx+c$.

Calculation: first substitute the value of slope in the equation,

Since $m=-\frac{3}{2}$ , so substitute it in the equation,

  $\begin{array}{l}y=mx+c\\ y=-\frac{3}{2}x+c\text{ [substitute }m=-\frac{3}{2}]\end{array}$

Now find the value of $c$ , substitute $x=-3,y=5$

  $\begin{array}{l}y=-\frac{3}{2}x+c\\ 5=-\frac{3}{2}\left(-3\right)+c\text{ [substitute }x=-3,y=5]\\ 5=\frac{9}{2}+c\text{ [multiply]}\\ c=\frac{1}{2}\text{ [subtract }\frac{9}{2}\text{ both side}]\end{array}$

Thus, the equation of the line is $y=-\frac{3}{2}x+\frac{1}{2}$.

b.

To determine

To find : the three additional points through the lines passes.

Answer to Problem 10RE

the points are $\left(0,\frac{1}{2}\right)$ , $\left(3,0\right)$ , $\left(2,-\frac{5}{2}\right)$.

Explanation of Solution

Given information :

Point is $\left(-3,5\right)$.

Slope of the line is $m=-\frac{3}{2}$.

Calculation: from the above part it can be observed that,

the equation of the line is $y=-\frac{3}{2}x+\frac{1}{2}$.

To find the points on this line, first substitute $x=0$ ,

  $\begin{array}{l}y=-\frac{3}{2}x+\frac{1}{2}\\ y=0+\frac{1}{2}\text{ [substitute]}\\ y=\frac{1}{2}\text{ [simplify]}\end{array}$

So the point is $\left(0,\frac{1}{2}\right)$.

Now, substitute $y=0$ ,

  $\begin{array}{l}y=-\frac{3}{2}x+\frac{1}{2}\\ 0=-\frac{3}{2}x+\frac{1}{2}\text{ [substitute]}\\ x=3\text{ [simplify]}\end{array}$

So the point is $\left(3,0\right)$.

Now , substitute $x=2$ ,

  $\begin{array}{l}y=-\frac{3}{2}x+\frac{1}{2}\\ y=-\frac{3}{2}\left(2\right)+\frac{1}{2}\text{ [substitute]}\\ y=-\frac{5}{2}\text{ [simplify]}\end{array}$

So the point is $\left(2,-\frac{5}{2}\right)$.

Thus, the points are $\left(0,\frac{1}{2}\right)$ , $\left(3,0\right)$ , $\left(2,-\frac{5}{2}\right)$.