Math Problem Statement

The points given in the table lie on a line. Find the slope of the line.    x

–1

2

5

8

y

3

–1

–5

–9

Solution

To find the slope of a line given points, we use the slope formula:

m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1}

From the table, we can use any two points to find the slope. Let’s use the points (1,3)(-1, 3) and (2,1)(2, -1):

m=132(1)=42+1=43m = \frac{-1 - 3}{2 - (-1)} = \frac{-4}{2 + 1} = \frac{-4}{3}

Thus, the slope of the line is:

43\boxed{-\frac{4}{3}}

Would you like me to verify using other pairs of points? Let me know if you have additional questions!

Related Questions

  1. How can we determine if other points lie on the same line?
  2. What is the equation of the line in slope-intercept form?
  3. How would the slope change if the table’s points were adjusted?
  4. How do we interpret a negative slope in this context?
  5. What role does slope play in linear equations?

Tip: Always double-check calculations by testing multiple points on the line!

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Math Problem Analysis

Mathematical Concepts

Linear Algebra
Slope of a Line

Formulas

{"Slope formula":"m = (y2 - y1) / (x2 - x1)"}

Theorems

Linear relationship between points
Definition of slope in linear equations

Suitable Grade Level

Grades 8-10