Math Problem Statement

What is the equation of this line?

What is the equation of this line?

Solution

The graph shows a straight line, so the equation will be in the form of y=mx+by = mx + b, where:

  • mm is the slope (rate of change of the line).
  • bb is the y-intercept (the value of yy when x=0x = 0).

Step 1: Determine the slope (mm)

To calculate the slope, we can use two points on the line. From the image:

  • The line passes through the point (0,2)(0, -2) (the y-intercept).
  • Another point the line passes through is approximately (4,2)(4, 2).

The formula for slope is: m=y2y1x2x1m = \frac{y_2 - y_1}{x_2 - x_1} Substitute (x1,y1)=(0,2)(x_1, y_1) = (0, -2) and (x2,y2)=(4,2)(x_2, y_2) = (4, 2): m=2(2)40=44=1m = \frac{2 - (-2)}{4 - 0} = \frac{4}{4} = 1 So, the slope m=1m = 1.

Step 2: Determine the y-intercept (bb)

From the graph, the line crosses the y-axis at y=2y = -2. Thus, the y-intercept b=2b = -2.

Conclusion:

The equation of the line is: y=x2y = x - 2

Would you like further explanation or have any questions? Here are five related questions to expand on this:

  1. How do you find the equation of a line if you are given two points?
  2. What is the significance of the slope in a linear equation?
  3. How do parallel lines relate in terms of slope?
  4. How can we find the x-intercept of this line?
  5. How do you graph a line given its equation?

Tip: To quickly determine the slope visually, count the vertical and horizontal distance between two points on the line (rise over run).

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Graphing

Formulas

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

Theorems

Slope-Intercept Form

Suitable Grade Level

Grades 8-10