Examine the function, and determine whether or not it is written in standard form; standard form makes the equation conform to a y=mx+b pattern. Leave the equation alone if the y-variable is isolated on one side of the equal sign. However, rearrange the equation algebraically if y is being added to, subtracted from, divided by or multiplied by any other term. Make sure that on the side of the equation opposite the y-variable, the x-term appears before the (constant) number, if any.
Look at the x-variable of the function, and notice whether any number appears directly before it; for example, the number 4 appears before the x-variable in the function y=4x+3. Write down that number to the side and set it equal to the word "slope," or "m," as in m=4. Reexamine the function and identify the number, otherwise known as the y-intercept, that is being added to or subtracted from the x-term; in the example y=4x+3, the y-intercept would be 3. Write the y-intercept value below the slope value to the side, equal to either the word "intercept" or "b."
Take out your coordinate grid. Label each tick-mark of the y-axis from the origin, or zero, up and down to 10 and -10. Repeat the labeling for each tick of the x-axis, also out to 10 and -10. Look down at the y-intercept and count that many tick marks up or down the y-axis, up if the intercept is positive and down if negative, and draw a small circle, or point, at that location.
Look at the slope, or m, you previously identified. If the number is a whole, non-fractional number, draw a line under the number and add a one beneath the line, making the number a fraction (for example, 4 will become 4/1). Place your pencil on the y-intercept point you made on the y-axis of your coordinate plane. Count up the y-axis as many tick marks as the top of the slope fraction dictates; for example, 4 tick marks in the slope fraction 4/1. Count as many tick-marks to the right as the bottom of the fraction dictates. Make a point where your pencil comes to rest. Reverse the "up and to the right" formula to "down and to the right" if the slope is a negative number. Connect the y-intercept point with the new point with a straight-edge to finish the graph of the linear function.