Key Concepts

The first is by plotting points and then drawing a line through the points. The second is by using the y-intercept and slope. The third is applying transformations to the identity function f(x)=x f ( x ) = x .

The standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form. When an equation is given in this form, it’s pretty easy to find both intercepts (x and y). This form is also very useful when solving systems of two linear equations.

1. Find three points whose coordinates are solutions to the equation. Organize them in a table.
2. Plot the points in a rectangular coordinate system. Check that the points line up.
3. Draw the line through the three points. Extend the line to fill the grid and put arrows on both ends of the line.

When the equation has a homogeneous variable (i.e. only one variable), then this type of equation is known as a Linear equation in one variable….Formulas.

The linear equation has only one variable usually and if any equation has two variables in it, then the equation is defined as a Linear equation in two variables. For example, 5x + 2 = 1 is Linear equation in one variable. But 5x + 2y = 1 is a Linear equation in two variables.

Answer: B. 33 ( x + y ) is not a linear equation in one variable. This is because there are two variables x and y in the given equation.

What is the difference between linear and exponential functions? Linear functions change at a constant rate per unit interval. An exponential function changes by a common ratio over equal intervals.

If the growth or decay involves increasing or decreasing by a fixed number, use a linear function. The equation will look like: y = mx + b f(x) = (rate) x + (starting amount). If the growth or decay is expressed using multiplication (including words like “doubling” or “halving”) use an exponential function.

In linear functions, rate of change is constant: as x goes up, y will go up a consistent amount. In exponential functions, the rate of change increases by a consistent multiplier—it will never be the same, but there will be a pattern.

What is another word for exponential?

Logarithmic growth is the inverse of exponential growth and is very slow. A familiar example of logarithmic growth is a number, N, in positional notation, which grows as logb (N), where b is the base of the number system used, e.g. 10 for decimal arithmetic.

Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function.