The Slope and Y -Intercept of the Line $y = m x + b$

question 25

Multiple Choice

The slope and y -intercept of the line $y = m x + b$ that best fits the three noncollinear points $( 2,2 ) , ( 3,3 )$ and $( 5,4 )$ are given by the solution of the following system of linear equations. $\left\{ \begin{array} { c } 77 m + 12 b = 46 \\12 m + 5 b = 8\end{array} \right.$ Solve the system and find the equation of the best-fitting line. Round parameters to the nearest thousandth.

• A) \(y = 0.415 x + 1.188\)
• B) \(y = 0.412 x - 1.188\)
• C) \(y = 0.417 x + 1.188\)
• D) \(y = 0.556 x + 0.266\)
• E) \(y = 0.42 x + 1.188\)

---

Definitions:

Cognitive Triad

A concept in cognitive therapy that describes a pattern of thinking involving negative views about the self, the world, and the future.

Object Relations

A theory in psychoanalysis focusing on the relationships between individuals and the external objects (often other people) that represent significant others in one’s life.

Sociocultural

Pertaining to the combination of social and cultural factors that influence an individual's behavior and experiences.

Theoretical Orientation

A foundational perspective or set of principles that guides a therapist's approach to understanding and treating psychological issues.