Math Problem Statement

solve for both equations

Solve for the equations of the lines that pass through the points (3, 1) and (0, -3) for line 1, and (-1, -5) and (4, -2) for line 2.

Solution

Here are the equations of the two lines based on the given points:

  1. Line 1 (through points (3,1)(3, 1) and (0,3)(0, -3)): y=1.33x3y = 1.33x - 3

    • Slope (mm): 1.33
    • Intercept (bb): -3
  2. Line 2 (through points (1,5)(-1, -5) and (4,2)(4, -2)): y=0.6x4.4y = 0.6x - 4.4

    • Slope (mm): 0.6
    • Intercept (bb): -4.4

Would you like more details or have any questions?

Here are five related questions:

  1. How do you find the slope of a line from two points?
  2. How can you verify if a point lies on a line equation?
  3. What is the difference between slope-intercept and point-slope form?
  4. How do parallel lines relate in terms of their slopes?
  5. What is the geometric interpretation of the y-intercept?

Tip: The slope of a line represents the rate of change of y with respect to x, or the steepness of the line.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Slope-Intercept Form

Formulas

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

Theorems

Two-point form of a line
Slope-Intercept form

Suitable Grade Level

Grades 8-10