Math Problem Statement

In the regression line 𝑦=βˆ’10+3π‘₯ :

The 𝑦 -intercept =0 and the slope =3 . The 𝑦 -intercept =βˆ’10 and the slope =3 . The 𝑦 -intercept =3 and the slope =βˆ’10 . The 𝑦 -intercept =βˆ’10 and the slope =βˆ’3 . The 𝑦 -intercept =10 and the slope =3 .

Solution

In the regression line equation y=βˆ’10+3xy = -10 + 3x, the general form is y=mx+by = mx + b, where:

  • mm represents the slope of the line,
  • bb represents the y-intercept, which is the value of yy when x=0x = 0.

From the given equation y=βˆ’10+3xy = -10 + 3x:

  • The slope m=3m = 3,
  • The y-intercept b=βˆ’10b = -10.

So, the correct statement is:

The y-intercept = -10 and the slope = 3.

Would you like any more details or explanations? Here are some related questions to think about:

  1. How does the slope of a line affect its direction?
  2. What is the significance of the y-intercept in a real-world context?
  3. How would the line change if the slope were negative?
  4. Can you rewrite the equation in terms of xx instead of yy?
  5. How would you find the x-intercept of the line?

Tip: In regression, the slope represents the rate of change, and the y-intercept is the starting value when the independent variable is zero.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Regression
Slope-Intercept Form

Formulas

y = mx + b (Slope-Intercept Form)

Theorems

Slope-Intercept Theorem

Suitable Grade Level

Grades 8-10