Math Problem Statement

Which equation can be used to describe the relationship between x and y shown in the graph?

Solution

To determine which equation best describes the graph, let’s analyze the given line:

  1. Identify the slope:
    The line moves upwards as you move to the right, which indicates a positive slope. Therefore, the slope is positive, which eliminates options A, B, and C, because their slopes are negative.

  2. Y-intercept:
    The line crosses the y-axis at -4. This means the y-intercept (b) is -4.

  3. Equation of the line:
    The standard form of a linear equation is:
    y=mx+by = mx + b where mm is the slope and bb is the y-intercept.
    Since the slope is positive and the y-intercept is -4, the equation becomes:
    y=5x4y = 5x - 4

Correct Answer: D. y=5x4y = 5x - 4


Let me know if you would like a breakdown of how to calculate slope or additional details!

Here are 5 related questions for practice:

  1. How do you calculate the slope of a line given two points?
  2. What is the slope-intercept form of a linear equation?
  3. How do you determine the y-intercept from a graph?
  4. How can you tell if a slope is positive or negative just by looking at the graph?
  5. How do you graph a line given its equation?

Tip: A positive slope means the line rises as you move to the right, while a negative slope means it falls.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Slope-Intercept Form
Graphing Lines

Formulas

Slope-intercept form: y = mx + b

Theorems

Slope-Intercept Properties

Suitable Grade Level

Grades 8-10