Math Problem Statement

The points in the table lie on a line. Find the slope of the line. The points are (-1, -4), (0, -1), (1, 2), (2, 5).

Solution

To find the slope of the line passing through the points in the table, we can use the slope formula:

slope=y2y1x2x1\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}

Using any two points from the table, let’s take (1,4)(-1, -4) and (0,1)(0, -1):

slope=1(4)0(1)=1+40+1=31=3\text{slope} = \frac{-1 - (-4)}{0 - (-1)} = \frac{-1 + 4}{0 + 1} = \frac{3}{1} = 3

Thus, the slope of the line is 3.

Would you like more details or have any questions?

Here are five related questions:

  1. How would the slope change if one of the points had a negative x-value and positive y-value?
  2. Can you use the same formula to find the slope between other pairs of points in the table?
  3. How does the slope of a vertical line differ from that of a horizontal line?
  4. What is the equation of the line that passes through these points with the slope we found?
  5. Can the slope be determined from any two distinct points on a line?

Tip: When calculating slope, always check that you correctly subtract the coordinates, keeping the order consistent for both xx and yy values.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

Slope formula: (y2 - y1) / (x2 - x1)

Theorems

Slope of a Line

Suitable Grade Level

Grades 6-8