In the regression line 𝑦=−10+3𝑥
:

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

In the regression line equation \( y = -10 + 3x \), the general form is \( y = mx + b \), where:

- \( m \) represents the slope of the line,
- \( b \) represents the y-intercept, which is the value of \( y \) when \( x = 0 \).

From the given equation \( y = -10 + 3x \):

- The **slope** \( m = 3 \),
- The **y-intercept** \( b = -10 \).

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 \( x \) instead of \( y \)?
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.

In the regression line y = −10 + 3x, what is the correct y-intercept and slope?

Learn how to interpret the slope and y-intercept in the regression line y = −10 + 3x. This problem focuses on linear regression and the slope-intercept form of a line. Suitable for students in Grades 8-10.

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