Math Problem Statement

Write an equation for the line graphed below.

Solution

Let's find the equation of the line from the graph you uploaded.

To do this, we need to identify the slope and the y-intercept.

  1. Find the slope (m): The slope of the line is the ratio of the change in y to the change in x (rise over run). From the graph, it looks like the line decreases by 2 units in y for every 1 unit it moves to the right in x. Therefore, the slope m=2m = -2.

  2. Find the y-intercept (b): The line crosses the y-axis at y=5y = 5, so the y-intercept b=5b = 5.

Now that we have the slope and the y-intercept, we can write the equation of the line in slope-intercept form:

y=mx+by = mx + b

Substituting the values of mm and bb:

y=2x+5y = -2x + 5

So, the equation of the line is:

y=2x+5y = -2x + 5

Would you like further details or clarification? Here are a few related questions to expand on this:

  1. How do you find the slope between two points?
  2. How do you convert the equation from slope-intercept form to standard form?
  3. What does the y-intercept represent in real-world contexts?
  4. How do you determine if two lines are parallel or perpendicular from their equations?
  5. How do you graph the equation y=2x+5y = -2x + 5 step-by-step?

Tip: The slope mm tells you how steep the line is, and the sign of mm (positive or negative) shows the direction of the line (up or down).

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Slope
Y-intercept

Formulas

y = mx + b

Theorems

Slope Formula
Intercept Theorem

Suitable Grade Level

Grades 6-8