Finding the Slope of a Line from its Equation

The slope of a line is a measure of its steepness and direction. For a linear equation given in the standard form \(Ax + By + C = 0\), there is a simple formula to determine its slope.

Understanding the Standard Form and Slope

A linear equation in two variables, x and y, can be written in the standard form:

\(Ax + By + C = 0\)

where A, B, and C are constants, and A and B are not both zero. The slope (m) of the line represented by this equation can be calculated using the formula:

\(m = -\frac{A}{B}\)

Applying the Formula to the Given Equation

The given equation of the line is:

\(4x + 3y - 4 = 0\)

Comparing this equation with the standard form \(Ax + By + C = 0\), we can identify the coefficients A and B:

• A is the coefficient of x, which is 4. So, \(A = 4\).
• B is the coefficient of y, which is 3. So, \(B = 3\).
• C is the constant term, which is -4. So, \(C = -4\). (Note: C is not needed to find the slope using this formula).

Now, we use the slope formula \(m = -\frac{A}{B}\):

\(m = -\frac{4}{3}\)

Calculating the Slope

Substituting the values of A and B into the formula, we get:

Slope \(m = -\frac{4}{3}\)

Thus, the slope of the line \(4x + 3y - 4 = 0\) is \(-\frac{4}{3}\).

Conclusion

The slope of the line \(4x + 3y - 4 = 0\) is \(-\frac{4}{3}\).