Math Problem Statement

Write an equation for the line graphed in the figure to the right.

Solution

To write the equation of the line in the graph, we can use the slope-intercept form of the equation of a line:

y=mx+by = mx + b

where:

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

Step 1: Find the slope mm

The slope of a line is the change in yy divided by the change in xx, which is calculated as:

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

Looking at the graph, I will select two points on the line:

  • Point 1: (2,4)(-2, -4)
  • Point 2: (2,4)(2, 4)

Now calculate the slope:

m=4(4)2(2)=4+42+2=84=2m = \frac{4 - (-4)}{2 - (-2)} = \frac{4 + 4}{2 + 2} = \frac{8}{4} = 2

So, the slope mm is 2.

Step 2: Find the y-intercept bb

The y-intercept is the point where the line crosses the y-axis. From the graph, we can see that the line crosses the y-axis at y=0y = 0.

Thus, b=0b = 0.

Final Equation

Now that we know m=2m = 2 and b=0b = 0, the equation of the line is:

y=2xy = 2x

Would you like further details or have any questions?


Here are some related questions:

  1. How do you calculate the slope of a line from its graph?
  2. What is the significance of the y-intercept in a linear equation?
  3. How do you convert from slope-intercept form to standard form?
  4. What does it mean if a line has a slope of zero?
  5. How can you determine if two lines are parallel based on their equations?

Tip: Always check if the line crosses the y-axis at zero, as that simplifies your equation greatly by eliminating the constant bb.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slope-Intercept Form

Formulas

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

Theorems

Slope-Intercept Theorem

Suitable Grade Level

Grades 8-10