# Linear Equations and Functions

## 9 terms · Chapter 5 notecards for algebra 1

### Direct Vaiation

A relationship between two variables in which one is a constant multiple of the other. In particular, when one variable changes the other changes in proportion to the first.

If b is directly proportional to a, the equation is of the form b = ka (where k is a constant).

### Linear Equation

A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable

### Slope

In mathematics, the slope or gradient of a line describes its steepness, incline, or grade. A higher slope value indicates a steeper incline. Slope is not defined for vertical lines.

Slope is normally described by the ratio of the "rise" divided by the "run" between two points on a line.

### Rise

The single or numerator on the top of a slope that shows how high a the slope rises. For example, m=2/1, 2 is the rise

### Run

The number in the denominator that shows how many points a slope moves horizontally. M=1/4, 4 is the run.

### X-Intercept

The x-intercepts are where the graph crosses the x-axis,

### Y-Intercept

the y-intercepts are where the graph crosses the y-axis.

### Slope intercept Form

The slope intercept form is probably the most frequently used way to express equation of a line. To be able to use slope intercept form, all that you need to be able to do is 1) find the slope of a line and 2) find the y-intercept of a line. In general, the slope intercept form assumes the formula: y= mx +b

### Standard Form

Standard form is a way of writing down very large or very small numbers easily. 103 = 1000, so 4 × 103 = 4000 . So 4000 can be written as 4 × 10³ . This idea can be used to write even larger numbers down easily in standard form.