Answer:
A linear equation is a fancy term for a straight line, which can be created by joining 2 points.
A point can be defined by (x, y), where x and y are the horizontal distance and the vertical distance respectively from point (0,0) (called the origin).
There are 3 ways to define a line:
(1) The slope-intercept form
y = mx + b, in which m is the slope, b is the y-intercept, where the line crosses the vertical axis at (0, b). If values of m and b are given, you can substitute and write the equation right away.
The slope, m, is calculated by rise (vertical difference between 2 points on the line) divided by run (horizontal difference between the 2 points on the line)
Explanation:
or example, if 2 points on the line are
(x1, y1) and (x2, y2)
Then slope = (y1– y2)/(x1 — x2)
If m > 0, then the line rises to the right.
If m = 0, then the line is horizontal.
If m < 0, then the line rises to the left.
If the line is in the form x = c, where c is a constant, then the line is vertical.
(2) Point slope form
m = (y — y1)/(x — x1), when (x1, y1) and m are given.
In other words,
m(x — x1) = y — y1
mx — m(x1) = y — y1
y = mx — m(x1) + (y1)
Note that b = -m(x1) + (y1)
(3) linear form
ax + by + c = 0, where a, b, and c are constants.