Math Problem Statement

Determine the equation of the straight line on the graph.

Solution

The graph shows a straight line, which suggests a linear equation. From a quick observation of the graph, we can determine the following:

  1. Slope (m): To find the slope, we can use two points on the line. The line seems to pass through the points (10,0)(-10, 0) and (10,8)(10, 8).

    Using the formula for slope: m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1} where (x1,y1)=(10,0)(x_1, y_1) = (-10, 0) and (x2,y2)=(10,8)(x_2, y_2) = (10, 8): m=8010(10)=820=0.4m = \frac{8 - 0}{10 - (-10)} = \frac{8}{20} = 0.4

  2. Y-intercept (b): The y-intercept is where the line crosses the y-axis. From the graph, the y-intercept seems to be (0,4)(0, 4).

  3. Equation of the line: Using the slope-intercept form of a line: y=mx+by = mx + b Substituting the slope m=0.4m = 0.4 and the y-intercept b=4b = 4, the equation of the line is: y=0.4x+4y = 0.4x + 4

Would you like a more detailed explanation or have any questions about the process?

Here are 5 related questions to deepen your understanding:

  1. How is the slope of a line determined using two points?
  2. What does the slope represent in the context of a graph?
  3. How do we interpret the y-intercept in real-world applications?
  4. Can the line equation change if we select different points?
  5. How would you find the x-intercept of this line?

Tip: When working with linear equations, the slope tells you how steep the line is, and the y-intercept shows where the line crosses the y-axis.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Graphing

Formulas

Slope formula m = (y2 - y1) / (x2 - x1)
Slope-intercept form y = mx + b

Theorems

The Slope Formula
The Slope-Intercept Form of a Line

Suitable Grade Level

Grades 8-10