Math Problem Statement

Find the slope of the line that passes through the points (4,0) and (6,2).

Solution

To find the slope mm of the line passing through the two points, we use the slope formula:

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

From the given points:

  • Point 1: (x1,y1)=(4,0)(x_1, y_1) = (4, 0)
  • Point 2: (x2,y2)=(6,2)(x_2, y_2) = (6, 2)

Substitute these values into the formula:

m=2064=22=1m = \frac{2 - 0}{6 - 4} = \frac{2}{2} = 1

Thus, the slope mm is 11.

Would you like more details or further clarifications?

Here are 5 related questions to consider:

  1. What is the significance of a slope value of 1 in a line's behavior?
  2. How would the slope change if Point 1 were (4,2)(4, 2) and Point 2 (6,0)(6, 0)?
  3. What does a slope of 0 mean for a line?
  4. How do you find the equation of the line once you have the slope and a point?
  5. Can you determine the y-intercept from the given information?

Tip: The slope of a line indicates the steepness or incline of the line. A positive slope means the line ascends, while a negative slope means it descends.

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Math Problem Analysis

Mathematical Concepts

Algebra
Coordinate Geometry

Formulas

Slope formula m = (y2 - y1) / (x2 - x1)

Theorems

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Suitable Grade Level

Grades 7-9