Linear Functions and Lines :
Here we are going to see, how to find slope and equation of a straight lines using the given information.
Consider a line in the coordinate plane, along with two points (x1,y1) and (x2,y2) on the line. Draw two right triangles with horizontal and vertical edges as in the figure below.
Thus the ratio (y2−y1) / (x2−x1) is a constant depending only on the line and not on the particular points (x1,y1) and (x2,y2) chosen on the line. This constant is called the slope of the line.
If (x1,y1) and (x2,y2) are any two points on a line, with x1≠x2, then the slope of the line is
(y2 − y1) / (x2 − x1)
The equation of a line, given its slope and one point on it :
The line in the xy-plane that has slope "m" and contains the point (x1, y1) is given by the equation
y − y1 = m(x − x1)
The equation of a line, given two points on it :
The line in the xy-plane that contains the points (x1,y1) and (x2,y2), where x1 ≠ x2, is given by the equation
(y − y1) / (y2 − y1) = (x - x1) / (x2 − x1)
The equation of a line, given its slope and vertical axis intersection :
The line in the xy-plane with slope m that intersects the y-axis at (0, b) is given by the equation
y = mx + b.
Linear functions :
A linear function is a function f of the form
f(x) = mx + b,
where m and b are constants
Constant functions :
A constant function is a function f of the form
f(x) = b,
where b is a constant.
After having gone through the stuff given above, we hope that the students would have understood "Linear Functions and Lines".
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