I don't get y=m(x) + b

Question

I don't get how  you do x y coordinates

 

Answer 1

The coordinate plane consists of a vertical (up and down) line called the y axis and a horizontal (left and right) line called the x axis. The center of the coordinate plane (also called the origin) is the point both the horizontal horizontal x coordinate and the vertical y coordinate are both zero. A point is represented as (x,y) where the horizontal x coordinate is the 1st value in parens followed by a comma and then by the 2nd value in parens - the vertical y coordinate. The x values to the left of the origin are negative values and the x values to the right of the origin are positive values. The y values belowe the origin are negative values and the y values above the origin are positive values. The equation (y = mx + b) is the equation of a straight line expressed in slope intercept form. The slope (m) of a line is the ratio of the change in vertical distance to the change in horizontal distance between any two points on the line. The intercept (b) of a line is the point where the line intercepts (crosses) the y axis, i.e. the value of y when x = 0. The slope formula (ratio) of a line is (y2 - y1) / (x2 - x1) where any two points on the line are expressed as (x1,y1) and (x2,y2).

Answer 2

When graphing, first we need to know what we're looking at. A simple graph will consist of long horizontal line called the x-axis, and long vertical line called the y-axis. Where these two lines meet is the origin with coordinates of (0,0). If you move from the origin the coordinates begin to change depending on the direction. Right and Left along the x-axis is positive and negative; respectively. Up and Down along the y-axis is positive and negative; respectively.

Coordinates denote how far a point is from the axis lines. So coordinates of (4,8) are four units right (along the x-axis) and eight units up (along the y-axis). Or (-3, 2) would be three units left and two units up.

After understanding what a graph is, we need to make it function for us. There are many applications for graphing that I won't discuss now, however when we have points on a graph we usually want to know their relationship. The relationship of points in a graph can be understood by the equation that represents them. That is to say, given any two points on a graph, how did we get from one to the next?

Linear equations are the first step to understanding how graphing works.  y = mx + b is the simplest equation used for graphing. This equation is the slope-intercept form for straight lines where 'm' represents the slope of the line, and 'b' represents the y-axis intercept (when x = 0, y = b).

If the graph is a flat (horizontal line) it has a slope of zero [y=b], and b is where the line crosses the y-axis.

Finally, graphing becomes what you want to achieve with it. If you're given values or coordinates you could determine the equation. If you're given the equation you could find points on that line by substitution. There are more complicated equations that look like waves, and those that have multiple dimensions; and you'll get to those in years to come.

I hope this response answers your question. If you have a more specific concern feel free to post it.

Answer 3

 y = mx + b    ==>   this is the slope-intercept form of linear equations, where 'm' is the slope of the line and 'b' is the y-intercept which is the point at which the line crosses the y-axis (i.e., the y-value when x=0).

If you are looking to find x,y-coordinates of a line given a linear equation in slope-intercept form, the simplest way would be to pick x-values and find the y-values associated with each of these x-values by plugging them into the equation.

For instance, 

   at  x = 0 ,     y = m(0) + b = 0 + b = b     ==>     (x, y) = (0, b)

   at  x = 1 ,     y = m(1) + b = m + b          ==>     (x, y) = (1, m+b)

   at  x = 2 ,     y = m(2) + b = 2m + b        ==>     (x, y) = (2, 2m+b)

...and so on...