# How to Find an Equation Given a Table of Numbers

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Mathematical equations are essentially relationships. A line equation describes the relationship between ​x​ and ​y​ values found on a coordinate plane. The equation of a line is written as ​y=mx​+​b​, where the constant ​m​ is the slope of the line, and the ​b​ is the ​y​-intercept. One of the common algebraic problem questions asked is how to find the line equation from a set of values, such as a table of numbers that correspond to the coordinates of points. Here how to solve this algebraic challenge.

## Understand the Values in the Table

The numbers in a table are often the ​x​ and ​y​ values that are true for the line, which means the ​x​ and ​y​ values correspond to the coordinates of points on the line. Given that a line equation is ​y=mx​+​b​, the ​x​ and ​y​ values are numbers that can be used to arrive at the unknowns, such as the slope and the y-intercept.

## Find the Slope

The slope of a line – represented by ​m​ – measures its steepness. Also, the slope gives clues to the direction of the line in a coordinate plane. The slope is constant in a line, which explains why its value can be calculated. The slope can be determined from the ​x​ and ​y​ values provided in a given table. Remember that the ​x​ and ​y​ values correspond to points on the line. In turn, calculating a line equation’s slope requires the use of two points, such as point A (​x1, ​y1) and point B (​x2, ​y2). The equation to find the slope is

m = \frac{y_2-y_1}{x_2-x_1}

to solve for the term ​m​. Notice from this equation that the slope represents the change in ​y​-value per unit of change in the ​x​-value. Let’s take the example of the first point, A, being (2, 5) and the second point, B, being (7, 30). The equation to solve for the slope then becomes

m = \frac{30-5}{7-2} = \frac{25}{5} = 5

## Determine the Point Where the Line Crosses the Vertical Axis

After solving for the slope, the next unknown to solve for is the term ​b​, which is the ​y​-intercept. The ​y​-intercept is defined as the value where the line crosses the ​y​-axis of the graph. To arrive at the ​y​-intercept of a linear equation with a known slope, substitute in the ​x​ and ​y​ values from the table. Since the previous step above showed the slope to be 5, substitute the values of point A (2, 5) into the line equation to find the value of ​b​. Thus, ​y=mx​+​b​ becomes

5=(5 × 2)+b =10+b

so that the value of ​b​ is −5.