Math Problem Statement

Graph the points (-4, 5) and (5, -3) and draw a straight line that passes through both of them. Then answer the following questions.

Does the graph of (1, 0) lie on the line?

Does the graph of (1, -2) lie on the line?

Does the graph of (-3, 4) lie on the line?

Does the graph of (-5, -2) lie on the line?

Solution

The graph of the line passing through the points (-4, 5) and (5, -3) has been drawn. Here are the results regarding whether the given points lie on the line:

  1. Does the point (1, 0) lie on the line?
    No, it does not lie on the line.

  2. Does the point (1, -2) lie on the line?
    No, it does not lie on the line.

  3. Does the point (-3, 4) lie on the line?
    No, it does not lie on the line.

  4. Does the point (-5, -2) lie on the line?
    No, it does not lie on the line.

Let me know if you'd like more details or have any questions.

Here are 5 related questions:

  1. How do you calculate the slope between two points?
  2. What is the equation of a line given two points?
  3. How do you determine if a point lies on a given line?
  4. How can you find the y-intercept from two points on a line?
  5. How do parallel lines differ in terms of slope?

Tip: To check if a point lies on a line, substitute its coordinates into the line's equation and see if both sides match.

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Linear Equations

Formulas

Slope formula: (y2 - y1) / (x2 - x1)
Equation of a line: y = mx + b
Point-slope form of a line: y - y1 = m(x - x1)

Theorems

Two-point form theorem
Point-slope theorem

Suitable Grade Level

Grades 8-10