2. Graphs of Linear Functions
It is very important to know how to quickly sketch straight lines. When we use math to model real-world problems, it is worthwhile to have a sense of how straight lines "work" and what they look like.
We met this topic before in the Plane Analytical Geometry section. The following section serves as a reminder for you...
a. Slope-Intercept Form of a Straight Line: y = mx + c
If the slope (also known as gradient) of a line is m, and the 
-intercept is c, then the equation of the line is written:
y = mx + c
Example:
The line y = 2x + 6 has slope m = 2 and y-intercept c = 6.
b. Intercept Form of a Straight Line: ax + by = c
Often a straight line is written in the form ax + by = c. One way we can sketch this is by finding the x- and y-intercepts and then joining those intercepts.
Example:
Sketch the line 3x + 2y = 6.
Slope of a Line
The slope (or gradient) of a straight line is given by:
We can also write the slope of the straight line passing through the points (x1, y1) and (x2, y2) as:
Using this expression for slope, we can derive the following.
c. Point-slope Form of a Straight Line: y − y1 = m(x − x1)
If a line passes through the point (x1, y1) and has slope m, then the equation of the line is given by:
y − y1 = m(x − x1)
Example:
Find the equation of the line with slope - 3, and which passes through (2, -4).
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