Math Problem Statement

What is the slope of the line?

Solution

To find the slope of the line in the graph you provided, we can use the formula for slope:

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

Looking at the graph, we can identify two points on the line. From the image, it seems the line passes through points (0,3)(0, 3) and (3,0)(3, 0).

Using these two points:

  • Point 1: (0,3)(0, 3)
  • Point 2: (3,0)(3, 0)

Now, apply the slope formula:

m=0330=33=1m = \frac{{0 - 3}}{{3 - 0}} = \frac{{-3}}{{3}} = -1

So, the slope of the line is 1-1.

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

Here are 5 related questions to explore:

  1. What does a negative slope indicate about the direction of a line?
  2. How do you find the equation of a line given the slope and a point?
  3. Can two different lines have the same slope? What does that imply?
  4. How does the slope change if the line is more vertical or more horizontal?
  5. What is the slope of a vertical line and a horizontal line?

Tip: When identifying points on a graph, it's easier to use points where the line crosses the grid lines (intersections) to avoid estimation errors.

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Math Problem Analysis

Mathematical Concepts

Slope
Coordinate Geometry
Linear Equations

Formulas

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

Theorems

Slope-intercept form of a line

Suitable Grade Level

Grades 7-9