how can u tell if a equation is liner?
if you mean linear,
it has a term of the form ax where a is a constant, and it has no higher powers of x.
More generally, it can be written in a variety of forms:
ax+by+c=0
ax+by=c
y=mx+b
y-k = m(x-h)
I'm sure your text covers it in some detail.
thanks steve
To determine if an equation is linear, you need to understand the characteristics of a linear equation.
A linear equation is an equation that can be written in the form: y = mx + b, where:
- y is the dependent variable (usually represented on the y-axis),
- x is the independent variable (usually represented on the x-axis),
- m is the slope of the line,
- b is the y-intercept, or the point where the line crosses the y-axis.
Here are a few ways to tell if an equation is linear:
1. Degree of Variables: In a linear equation, the highest power of the variable (usually x) is 1. For example, y = 2x + 3 is linear because the highest power of x is 1. If the equation includes variables with exponents or other mathematical operations such as square roots or exponentials, it is not linear.
2. Constant Rate of Change: In a linear equation, the slope (m) remains constant throughout the line. This means that the ratio of the change in y to the change in x is always the same. To determine the slope, you can compare the coefficients of the x-term. If the coefficients remain the same, the equation is linear. For example, in the equation y = 3x + 2, the coefficient of x is 3, indicating a constant rate of change.
3. Shape of Graph: The graph of a linear equation is always a straight line. If the graph of an equation forms a straight line when plotted on a Cartesian coordinate system, it is linear. Any curved or nonlinear shape indicates that the equation is not linear.
By analyzing the equation and considering these characteristics, you can determine whether the equation is linear or not.