How to Find the Intercepts and Slope of a Linear Equation

Graphing any kind of equation can be time consuming, which is probably why graphing calculators quickly become a math student's best friend. Calculators can do almost any kind of math problem for you these days, including graphing an equation and then telling you the slop of that equation, as well as the x and y intercepts. But what are you going do to if you have to find the slope of a linear equation and its x and y intercepts without the help of a calculator? Let me guide you through the steps to find the slope and intercepts of a linear equation so that if you ever find yourself in this situation you are prepared.

Instructions

Find the Slope of a Linear Equation

1. Learn that the slope of a linear equation can be expressed with the equation:S = (Y2-Y1) / (X2-X1). Note: The numbers in this equation that you see next to the variables are not to be multiplied or subtracted or anything else, they are simply there to denote that there is point "Y one" and point "Y two" as well as point "X one" and point "X two." Remember that the Ys go over the Xs in this equation by remembering "rise over run" will give you slope.

2. Select two points on an already graphed line, or by calculating two points by plugging in a value for one variable and solving for the other variable. Write down the coordinates for your two points. For an example we will use the equation 3x+5=y. Now, to get two points on this line plug in two different values for x and then solve for two different values for y, and then record these coordinates. (2,11) and (10, 35) are the two coordinates that I came up with when I plugged in 2 and 10 for x and then solved for y.

3. Plug your x and y values into the equation you learned in Step 1. Remember while you are doing this to keep X1 with Y1 and X2 with Y2! So, for the example in the previous step, plug in the coordinates and end up with an equation that looks like this: (35-11) / (10-2)It doesn't matter which point is (X1,Y1) or (X2, Y2).

4. Do the subtraction within the parentheses first because that is what the order of operations calls for, and then divide. For my equation I would end up with, 24/8 after doing my subtraction and then 3 after doing my division. So, the slope of the line that I was working with is 3.

Find the Intercepts of a Linear Equation

1. Plug 0 in for x and then solve for y to find the y-intercept. So, for the equation that we just found the slope of, 3x+5=y, we would plug in 0 for x and then solve for y:3(0)+5=y5=yThat means that the y-intercept of this linear equation is (0, 5).

2. Plug 0 in for y and solve for x to find the x-intercept. So, for the same equation we would do the following:3x+5=03x=-5 (subtracting 5 from both sides)x=-5/3 (dividing both sides by three)So, the x-intercept of this linear equation is (-5/3, 0).

3. Know that the linear equation crosses the x-axis at the x-intercept and the y-axis at the y-intercept. For the linear equation that we have been working with we now know that it crosses the x-axis at (-5/3, 0) and the y-axis at (0, 5).