Chapter 1.5, Problem 17STP

To determine

To calculate:To find the expression that would best describe the given graph:

Answer to Problem 17STP

Expression that best describes the graph is $y=4x-5$

Explanation of Solution

Given information:Graph is given as follows:

  

Calculation:

Let us name the points in below graph:

  

Now, ordered pair for point A is $\left(3,7\right)$

And, ordered pair for point B is $\left(5,15\right)$

Let’s us consider the equation $y=2x+1$

Substituting $\left(5,15\right)$ in above equation

  $\begin{array}{l}\Rightarrow 15=2\left(5\right)+1\\ \Rightarrow 15=10+1\\ \Rightarrow 15\ne 11\end{array}$

Since, point B does not satisfy equation $y=2x+1$ , hence this does not represent the graph

Let’s us consider the equation $y=5x-10$

Substituting $\left(5,15\right)$ in above equation

  $\begin{array}{l}\Rightarrow 15=5\left(5\right)-10\\ \Rightarrow 15=25-10\\ \Rightarrow 15=15\end{array}$

Since, point B satisfies equation $y=5x-10$ , hence this may represent the graph

Substituting $\left(3,7\right)$ in above equation

  $\begin{array}{l}\Rightarrow 7=5\left(3\right)-10\\ \Rightarrow 7=21-10\\ \Rightarrow 7\ne 11\end{array}$

Since, point A satisfies equation $y=5x-10$ , hence this does not represent the graph

Let’s us consider the equation $y=3x-2$

Substituting $\left(5,15\right)$ in above equation

  $\begin{array}{l}\Rightarrow 15=3\left(5\right)-2\\ \Rightarrow 15=15-2\\ \Rightarrow 15\ne 13\end{array}$

Since, point B does not satisfy equation $y=3x-2$ , hence this does not represent the graph

Let’s us consider the equation $y=4x-5$

Substituting $\left(5,15\right)$ in above equation

  $\begin{array}{l}\Rightarrow 15=4\left(5\right)-5\\ \Rightarrow 15=20-5\\ \Rightarrow 15=15\end{array}$

Since, point B satisfies equation $y=4x-5$ , hence this may represent the graph

Substituting $\left(3,7\right)$ in above equation

  $\begin{array}{l}\Rightarrow 7=4\left(3\right)-5\\ \Rightarrow 7=12-5\\ \Rightarrow 7=7\end{array}$

Since, point A satisfies equation $y=4x-5$ , hence this may represent the graph

Hence, expression that best describes the graph is $y=4x-5$