Math Problem Statement

Write an equation in standard form for the line that passes through the given points (-7, -8) and (-7, 4).

Solution

The problem asks to write an equation in standard form for the line passing through the points (7,8)(-7, -8) and (7,4)(-7, 4).

Step 1: Check if it's a vertical line

Notice that both points have the same xx-coordinate, 7-7. This means the line is vertical. For a vertical line, the equation is simply x=constantx = \text{constant}, where the constant is the common xx-coordinate.

Step 2: Write the equation

Since both points have x=7x = -7, the equation of the line is:

x=7x = -7

Standard Form

In general, the standard form of a line is Ax+By=CAx + By = C. For a vertical line like this, the equation x=7x = -7 can be written as:

1x+0y=71x + 0y = -7

or simply:

x=7x = -7

This is the equation of the line in standard form.

Would you like further clarification or have additional questions?

Here are some related questions:

  1. How would you write the equation of a horizontal line passing through two points?
  2. What is the slope of a vertical line?
  3. How does the equation of a line change if it is not vertical or horizontal?
  4. Can you convert this vertical line equation into slope-intercept form?
  5. How do you find the slope of a line between two non-vertical points?

Tip: For any vertical line, the slope is undefined, and the equation is always of the form x=constantx = \text{constant}.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Coordinate Geometry

Formulas

Equation of a vertical line: x = constant

Theorems

Concept of a vertical line (where all x-coordinates are the same)

Suitable Grade Level

Grades 8-10