Math Problem Statement

How is the equation of the given graph related to standard form Ax + By = C?

Solution

The question is asking how the equation of the given graph relates to the standard form Ax+By=CAx + By = C. Let's analyze the graph to form an equation in standard form.

From the image, we see that the line passes through the y-axis at y=5y = 5 and the slope appears to be horizontal (a flat line). This suggests that the line is a horizontal line, which means its equation will be of the form:

y=5y = 5

To express this in the standard form Ax+By=CAx + By = C, we can rewrite y=5y = 5 as:

0x+1y=50x + 1y = 5

Here, A=0A = 0 and B=1B = 1, so the equation is already in standard form:

0x+1y=50x + 1y = 5

Thus:

  • The simplest form of the equation is y=5y = 5.
  • In standard form, A=0A = 0 and B=1B = 1.

Would you like more details, or do you have any questions?

Here are 5 related questions to help expand on this concept:

  1. What is the general form of the equation for vertical lines?
  2. How do you find the slope of a line from a graph?
  3. How can we convert an equation in slope-intercept form to standard form?
  4. What happens to the values of AA, BB, and CC in standard form when the line is vertical?
  5. Can every linear equation be written in standard form?

Tip: In a horizontal line, the slope is always 0, which simplifies the equation to y=constanty = \text{constant}.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Graphing
Standard Form

Formulas

Standard form of a linear equation: Ax + By = C
Equation of a horizontal line: y = constant

Theorems

Linear Equation

Suitable Grade Level

Grades 8-10