Chapter 1.9, Problem 4STP

For Exercises $1-5,$ choose the correct letter.

Which equation represents the table shown?

F. $y=8.5x$

G. $y=8.5x+12.50$

H. $y=15x$

I. $y=15x+12.50$

To determine

To Select: The right option for theLinear equation.

Answer to Problem 4STP

y=8.5x

Option F is correct.

Explanation of Solution

Given information: It is given that table of values (15, 127.50), (25, 212.50) and (35, 297.50)

Formula used: Let’s use $y=mx+b$ where ‘ m’ is slope. ‘ b’ is y intercept.

Formula to find slope $m=\frac{y_2-y_1}{x_2-x_1}$

Calculation:

Let’s take two points on the line to find slope m .

Let’s take (15, 127.50) and (25, 212.50)

Slope $m=\frac{212.50-127.50}{25-15}$

  $=\frac{85}{10}$

=8.5

Plug in m as 8.5 into the $y=mx+b$ .

It gives

  $y=8.5x+b$

Now, take one point and plug in it for x and y to find value of ‘b’.

Let’s use (15, 127.50)

  $127.50=8.5(15)+b$

Solve the equation for ‘b’

  $127.50=127.5+b$

Subtract both sides 127.50

It gives $b=0$ .

So, equation is $y=8.5x$ .