Sorry its so long, but its simple..
Step-by-step explanation:
Linear equations are equations with two variables (usually x and y) in the first power (no exponants or square root signs).
The term linear equation comes from the fact that the graph of the equation is a line. Â There are an infinite number of ordered pairs that are correct for the equation, but there is only one x for each y and only one y for each x (except for vertical and horizontal lines).
There are several ways to write a linear equation, but the simplest is probably slope intercept. Â The slope intercept form of linear equations is given by the general formula y = mx + b. Â In this formula, y and x remain as the variables, but m and b are replaced with numbers.
When dealing with the slope intercept form of a line, m is the slope. Â To find the slope on a graph, choose two known points. Â Starting at the point on the left, count how much you go up or down to reach the second point. Â This becomes the numerator of the slope (the sign will be negative if you have to go down). Â Next, count how many places you move to the right. Â The becomes the denominator of the fraction. Â Now, reduce your fraction (if possible) and you have the slope.
Example: Â I have the points (0, 4) and (3, 6)
Going from the first point to the second point, I have to count up 2. Â The numerator in my fraction is 2.
Going from the first point to the second point, I have to count right 3. Â The denominator of my fraction is 3.
The slope (m) is 2/3.
Back to slope-intercept form...
The b in slope-intercept form is called the y-intercept. Â It is the value of y when x = 0. Â To find this value on a graph, just look at how high the line is when it crosses the y-axis (bold vertical line where x=0).
Example (cont'): Â I am still using the points (0, 4) and (3, 6)
Since the y-intercept is the value of y when x = 0, the y-intercept (b) of this line is 4.
Since I have the slope and y-intercept of the line, I can now write the answer in slope intercept form by substituting in my values for m and b.
m = 2/3, b = 4
y = 2/3 *x + 4
I am going to stop my answer at this point and give you a chance to look it over and see if it helped. Â I hope that I have at least cleared up a little of your confusion.