FIND THE EQUATION

Concept: A coordinate graph is a system for finding the location of a point, or several points, on a flat surface called a plane. A coordinate graph is formed from two axis lines that cross at a point called the origin. The horizontal line is the x-axis and the vertical line is the y-axis. Both lines are marked as number lines with the origin at zero. The axes divide the graph into four quadrants, labeled I, II, III, and IV.

Each point on the grid is named by two numbers, an x-coordinate and a y-coordinate. The x-coordinate is always written first; the y-coordinate is always written second. Together the coordinates are called an ordered pair and are enclosed in parentheses, separated by a comma like this: (x, y) .

To find the equation of a line, the slope-intercept form of a line is the format used. It is also called the “y = mx+b format.” In this formula, the variable m is the slope of the line. The variable b is the y coordinate of the y-intercept, the point at which the line crosses the y-axis. Reduce the slope to a whole number if possible. If not, leave the slope as a fraction.

Steps for Finding the Equation of a Line

Step 1 | Find the y-intercept of the line.
Step 2 | Find the slope of the line using the grid-unit counting method.
Step 3 | Use the slope-intercept form to write the equation. y = mx + b
Step 4 | Write the final answer.

IMPORTANT NOTE: When writing answers in this section using fractions, use the following format.

Example Write the equation of the line in y = mx + b format.

Step 1 | Find the y-intercept of the line. | (0, 5)
Step 2 | Find the slope of the line using the grid-unit counting method. | -9 5
Step 3 | Use the slope-intercept form to write the equation. y = mx + b | y = mx + b y = -9x/5 + 7
Step 4 | Write the final answer. | y = -9x/5 + 7