Math Problem Statement

What is the equation of the graph below?

Solution

Let's analyze the graph to determine the equation of the line.

The line appears to be straight, meaning the equation will be of the form y=mx+by = mx + b, where:

  • mm is the slope.
  • bb is the y-intercept (the value where the line crosses the y-axis).

Step 1: Identify the y-intercept

From the graph, we can see that the line crosses the y-axis at (0,1)(0, 1). Therefore, b=1b = 1.

Step 2: Determine the slope

To calculate the slope mm, we use two points on the line. The graph shows the line passing through the points (0,1)(0, 1) and (1,3)(1, 3).

The formula for slope is:

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

Substitute the points (0,1)(0, 1) and (1,3)(1, 3):

m=3110=21=2m = \frac{3 - 1}{1 - 0} = \frac{2}{1} = 2

Thus, the slope is m=2m = 2.

Step 3: Write the equation

Now that we have m=2m = 2 and b=1b = 1, the equation of the line is:

y=2x+1y = 2x + 1

Conclusion:

The correct answer is y=2x+1y = 2x + 1, which matches the first option.

Would you like further details or have any questions?

Here are 5 related questions for further practice:

  1. How do you determine the slope of a line from a graph?
  2. What is the significance of the y-intercept in the equation of a line?
  3. How would the equation change if the line had a negative slope?
  4. How can you verify if a point lies on a given line?
  5. What happens to the equation if the line shifts vertically?

Tip: Always check at least two points on the graph to ensure the accuracy of the slope calculation.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Graphing

Formulas

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

Theorems

Slope-Intercept Theorem

Suitable Grade Level

Grades 8-10