Math Problem Statement

A, B, and C are coordinates on the line y = x - 7. Use the table of values to find A, B, and C.

Solution

To find the coordinates AA, BB, and CC on the line y=x7y = x - 7 using the table of values, we follow these steps:

  1. The line equation given is y=x7y = x - 7.
  2. We have the xx values from the table: 1-1, 00, and 11.
  3. We need to find the corresponding yy values for these xx values using the equation y=x7y = x - 7.

Let's calculate the yy values for each xx:

  • For x=1x = -1: y=17=8y = -1 - 7 = -8 So, the coordinate AA is (1,8)(-1, -8).

  • For x=0x = 0: y=07=7y = 0 - 7 = -7 So, the coordinate BB is (0,7)(0, -7).

  • For x=1x = 1: y=17=6y = 1 - 7 = -6 So, the coordinate CC is (1,6)(1, -6).

Thus, the coordinates are:

  • A=(1,8)A = (-1, -8)
  • B=(0,7)B = (0, -7)
  • C=(1,6)C = (1, -6)

Would you like more details or have any questions about these calculations?

Here are five related questions for further practice:

  1. What would be the coordinate of a point on the line y=x7y = x - 7 if x=2x = 2?
  2. How would the equation change if the line was shifted up by 3 units?
  3. What is the slope of the line y=x7y = x - 7?
  4. Find the coordinates of a point on the line y=2x7y = 2x - 7 for x=1x = -1.
  5. What is the yy-intercept of the line y=x7y = x - 7?

Tip: To determine the slope and intercept of a linear equation in the form y=mx+by = mx + b, mm represents the slope and bb represents the yy-intercept.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Coordinate Geometry

Formulas

y = x - 7

Theorems

Slope-Intercept Form of a Line

Suitable Grade Level

Grades 6-8