Math Problem Statement

What is the slope of this line? Simplify your answer and write it as a proper fraction, improper fraction, or integer.

Solution

To calculate the slope of the line, we use the slope formula:

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

From the graph, the two points on the line are (0,7)(0, -7) and (5,1)(5, -1). Substituting these coordinates into the formula:

m=1(7)50m = \frac{-1 - (-7)}{5 - 0}

Simplify the numerator and denominator:

m=1+75=65m = \frac{-1 + 7}{5} = \frac{6}{5}

Thus, the slope of the line is:

65\boxed{\frac{6}{5}}

Would you like more details or have further questions?

Here are 5 related questions to deepen understanding:

  1. How is the slope related to the steepness of a line?
  2. What would the slope be if the line were horizontal or vertical?
  3. How can the slope formula be derived from similar triangles?
  4. What does a positive or negative slope indicate about a line's direction?
  5. How can you determine the slope from an equation like y=mx+by = mx + b?

Tip: Always simplify the fraction for slope to its lowest terms to ensure accuracy and clarity!

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Math Problem Analysis

Mathematical Concepts

Algebra
Coordinate Geometry
Slope Calculation

Formulas

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

Theorems

Properties of Linear Equations
Slope of a Line

Suitable Grade Level

Grades 6-8