Math Problem Statement

the slope

What is the slope of the line in the given graph?

Solution

To find the slope of the line in the given graph, we can apply the slope formula:

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

From the graph, we can identify two clear points on the line:

  • Point 1: (5,5)(-5, -5)
  • Point 2: (5,5)(5, 5)

Now, using the slope formula:

m=5(5)5(5)=5+55+5=1010=1m = \frac{{5 - (-5)}}{{5 - (-5)}} = \frac{{5 + 5}}{{5 + 5}} = \frac{10}{10} = 1

Therefore, the slope of the line is 1.

Would you like more details, or do you have any further questions?

Here are 5 related questions to explore:

  1. How can we determine the y-intercept from this graph?
  2. What is the equation of the line in slope-intercept form?
  3. How would the graph look if the slope were negative?
  4. How do you find the slope if only one point is given?
  5. What does a slope of 0 represent on a graph?

Tip: The slope can tell us how steep a line is and in which direction it moves (positive slope means it rises from left to right).

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slope

Formulas

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

Theorems

Concept of slope in coordinate geometry

Suitable Grade Level

Grades 7-9