SAT Mathematics : Graphical Representation of Functions
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Example Question #9 : Graphing Linear Equations
What is the area of the triangle formed by the lines 
45
15
6
48
45
In order to find the area of the triangle, we can use relevant points such as the point of intersection and the x intercepts. In this case, the point of intersection is the point at which the equations of the lines are equal. So, if
then x = 4, and if we plug 4 back into our equation we can see that y = 6. So, the point of intersection is (4, 6).
If we set y = 0 for each equation, we can also find the x intercepts, in this case, (1, 0) and (16, 0).
The triangle will appear as follows
At this point, we can use the x intercepts to find the base, 16-1 or 15, and the point of intersection to find the height, in this case 6.
If the area of a triangle is
we can fill in the unknowns with
to arrive at an area of 45.
Example Question #10 : Graphing Linear Equations
The equation 3x+2y=6 represents a line. This line does NOT pass through which of the four quadrants?
III
I
IV
II
III
We can quickly visualize this line to draw conclusions.
In order to do so, plug in 0 for x to find a point on the line:
3(0)+2y=6
y=3
Thus, (0,3) is a point on the line.
Plug in 0 for y to find a second point on the line:
3x+2(0)=6
x=2
(2,0) is another point on the line.
Now we know that the line passes through the points (2,0) and (0,3).
A quick sketch of the two points reveals that the line passes through all but the third quadrant.
*note - a line with a positive slope will always pass through quadrants I and III, while a line with a negative slope will always pass through quadrants II and IV.*
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