Chapter 2: Q23. (page 86)

Which line best fits the data in the graph at the right?
$\begin{array}{l} A) y = x \\ B) y = - 0.5 x + 4 \\ C) y = - 0.5 x - 4 \\ D) y = 0.5 + 0.5 x \end{array}$

Short Answer

Expert verified

The correct option is $D) 0.5 + 0.5 x$ .

Step by step solution

Step-1 – Determine the points.

The coordinates of the points are $(1, 0.5), (2, 1.5), (3, 2), (4, 2.5)$

Step-2 – Calculate the slope of the line.

The slope is positive so all options with negative slope must be incorrect.

Take any two points and determine the equation except the points $(1, 0.5)$ .

Let the points are $(2, 1.5) a n d (3, 2)$ .

Substitute $(x_{1} y_{1}) = (2, 1.5) a n d (x_{2} y_{2}) = (3, 2)$ into the formula $s l o p e = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

$\begin{array}{l} m = \frac{2 - 1.5}{3 - 2} \\ m = 0.5 \end{array}$

Step-3 – Make the equation.

Substitute $(x_{1} y_{1}) = (2, 1.5)$ into $y - y_{1} = m (x - x_{1})$ .

localid="1647259272468" $\begin{array}{l} y - 1.5 = 0.5 (x - 2) \\ y - 1.5 = 0.5 x - 1 \\ y = 0.5 x + 0.5 \end{array}$

From the given options the only possible match can be option $D) 0.5 + 0.5 x$ .

Thus, the line best fits the data in the graph should be $D) 0.5 + 0.5 x$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Which line best fits the data in the graph at the right?
$\begin{array}{l} A) y = x \\ B) y = - 0.5 x + 4 \\ C) y = - 0.5 x - 4 \\ D) y = 0.5 + 0.5 x \end{array}$

Short Answer

Step by step solution

Step-1 – Determine the points.

Step-2 – Calculate the slope of the line.

Step-3 – Make the equation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Mechanics Maths

Decision Maths

Geometry

Probability and Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Which line best fits the data in the graph at the right?A) y=xB) y=−0.5x+4C) y=−0.5x−4D) y=0.5+0.5x

Short Answer

Step by step solution

Step-1 – Determine the points.

Step-2 – Calculate the slope of the line.

Step-3 – Make the equation.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Mechanics Maths

Decision Maths

Geometry

Probability and Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

Which line best fits the data in the graph at the right?
$\begin{array}{l} A) y = x \\ B) y = - 0.5 x + 4 \\ C) y = - 0.5 x - 4 \\ D) y = 0.5 + 0.5 x \end{array}$