**In graphing linear equation, there are some formulas:
y = mx + b: slope intercept form
With:
x,y: variables
b: y-intercept
m: slope.
m =
*All y-intercept forms are developed from the simplest form: y = x
After that, the coefficient m in front of x is added, known as the slope or stretching number. When m is positive, the line rises; when m is negative, the line descends. The greater m is, the steeper the line gets and vice versa.
Then, b is added to the equation, known as the y-intercept or sliding number. The value of b indicates the point where the line intercepts with the y-axis; in other words, changing the value of b will shift the line accordingly on the xy-plane without changing the slope of the line.
**Graphing:
– If the line is not in the slope-intercept form, change it into slope-intercept form.
– Plot the y-intercept as the point (0,b).
– Plot the second point using the slope, m, or starting from the first point. If “rise” is positive, move up; otherwise, move down. If the “run” is positive, move to the right; if it is negative, move to the left.
– Draw a line through the y-intercept and the second point to complete graphing.
*** If the xy-plane is not big enough to contain the y-intercept, predict the area where the line goes through, then calculate the y value by substitute x with a value in that area in order to get the points or vice versa.
*Example: y = 2x + 10
Since the y-axis only contains the value from -2 to 3, the y-intercept cannot be plotted. Moreover, the y-axis is limited more than the x-axis, so it is better to calculate the x value by substitute the y value.
With:
y = 0, x = -5 -> (-5,0)
y = 2, x = -4 -> (-4,2)
Plot these points on the xy-plane then connect them to form the line.