Math Problem Statement

The point (a, 2) lies on the line whose equation is 2x + y + 4 = 0. What is the value of a?

Solution

We are given the equation of a line:

2x+y+4=02x + y + 4 = 0

The point (a,2)(a, 2) lies on this line, and we need to find the value of aa.

Step-by-Step Solution:

  1. Substitute the coordinates of the point (a,2)(a, 2) into the equation of the line. Here, x=ax = a and y=2y = 2.

2a+2+4=02a + 2 + 4 = 0

  1. Simplify the equation:

2a+6=02a + 6 = 0

  1. Solve for aa:

2a=62a = -6

a=3a = -3

Thus, the value of aa is 3\boxed{-3}, which corresponds to option (B).

Would you like more details or explanations?


Here are 5 related questions to extend your understanding:

  1. What is the general form of a linear equation in two variables?
  2. How can we determine the slope of the line from the equation 2x+y+4=02x + y + 4 = 0?
  3. If the point (x,y)(x, y) lies on a line, how do you check if the equation is satisfied?
  4. What is the y-intercept of the line 2x+y+4=02x + y + 4 = 0?
  5. How do you find the distance between a point and a line?

Tip: When solving for a variable, always substitute known values first to simplify the equation.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Algebra

Formulas

General form of linear equation: Ax + By + C = 0

Theorems

Substitution Method

Suitable Grade Level

Grades 7-9