Chapter 8, Problem 2STP

To determine

To find: equation which is true for the given ordered pair

Answer to Problem 2STP

The correct equation that satisfies each ordered pair is: G

Explanation of Solution

Given:

x	y
0	0
1	42.50
2	85
3	127.5

F $y=37.5x+5$

H $y=27.5x+15$

G $y=42.5x$

J $y=37.5x+10$

Formula used:

Slope of the line is calculated by

  $m=\frac{y_2-y_1}{x_2-x_1}$

Calculation:

The general form of equation of line in point-slope intercept form is:

  $y-y_1=m\left(x-x_1\right)$

Here, m represents slope and $\left(x_1,y_1\right)$ are given points.

Step 1: Find slope of the line ( m ) by using formula of two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$

  $m=\frac{y_2-y_1}{x_2-x_1}$

Consider the coordinates of any two points: $\left(x_1,y_1\right)=\left(1,42.50\right)$ and $\left(x_2,y_2\right)=\left(2,85\right)$

Put the value in slope formula:

  $\begin{array}{c}m=\frac{85-42.50}{2-1}\\ =\frac{42.50}{1}\\ =42.50\end{array}$

Step 2: To write the equation, use the slope and coordinates of any point.

So, put the value of $\left(x_1,y_1\right)=\left(1,42.50\right)$ and $m=42.50$ in formula.

  $y-42.50=42.50\left(x-1\right)$

Solve the bracket.

  $y-42.50=42.50x-42.50$

Add both sides of equation by 42.50.

  $\begin{array}{c}y-42.50+42.50=42.50x-42.50+42.50\\ y=42.5x\end{array}$

Conclusion:

Therefore, the correct equation that satisfies each ordered pair is: G