Chapter 1.3, Problem 33AYU

To determine

To locate: three points on the line

Answer to Problem 33AYU

First solution, the additional points are: $\left(4,-7\right),\left(6,-10\right)and\left(8,-13\right)$

Second solution, the additional points are: $\left(0,-1\right),\left(-2,2\right)and\left(-4,5\right)$

Explanation of Solution

Given:

Slope: $-\frac{3}{2}$

Point: $\left(2,-4\right)$

Calculation:

To graph a line from point and slope $\left(m\right)$

The point is $\left(2,-4\right)$ and $-\frac{3}{2}$

Note that: $Slope=\frac{rise}{run}$

That is mean that for every horizontal movement $\left(run\right)$ there will be a vertical movement $\left(rise\right)$ .

a point $\left(2,-4\right)$ and it's slope.

  $\therefore$ The slope = $-\frac{3}{2}$

Now, the two applicable solutionsare $m=-\frac{3}{2}$ .

  $\therefore$ The slope = $-\frac{3}{2}$

Now, the two applicable solutions are

First, if the slope is $m=-\frac{3}{2}$

That is mean that for every horizontal movement $\left(run\right)$ of $\left(2\right)$ unit to the right there will be a vertical movement of $\left(-3\right)$ units downward.

Now, apply this on each point as follows:

(1) Start at the given point $\left(2,-4\right)$ and move $1$ unit to the right and $4$ units up, the point $\left(4,-7\right)$ is reached.

(2) Startat the point $\left(4,-7\right)$ and move $1$ unit to the right and $4$ units up, the point $\left(6,-10\right)$ is reached.

(3) Startat the point $\left(6,-10\right)$ and move $1$ unit to the right and $4$ units up, the point $\left(8,-13\right)$ is reached.

  

Second, if the slope is $m=\frac{3}{-2}$

That is meant that for every horizontal movement (run} of $\left(-2\right)$ unit to the left there will be a vertical movement of $\left(3\right)$ units upward.

Now, apply this on each point as follows:

(1) Start at the given point $\left(2,-4\right)$ and move $1$ unit to the right and $4$ units up, the point $\left(0,-1\right)$ is reached.

(2) Start at the point $\left(0,-1\right)$ and move $1$ unit to the right and $4$ units up, the point $\left(-2,2\right)$ is reached.

(3) Start at the point $\left(-2,2\right)$ and move $1$ unit to the right and $4$ units up, the point $\left(-4,5\right)$ is reached.

  

Result:

First solution, the additional points are: $\left(4,-7\right),\left(6,-10\right)and\left(8,-13\right)$

Second solution, the additional points are: $\left(0,-1\right),\left(-2,2\right)and\left(-4,5\right)$

Conclusion:

First solution, the additional points are: $\left(4,-7\right),\left(6,-10\right)and\left(8,-13\right)$

Second solution, the additional points are: $\left(0,-1\right),\left(-2,2\right)and\left(-4,5\right)$