SAT Math : How to find slope of a line
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Example Question #511 : Geometry
A line passes through the origin, and the points (1, k) and (k,4). What is a possible value for k?
To find k, first identify what is known.
The origin means the point (0,0).
Therefore the line passes through the points:
Since a line by definition has the same slope between the points, calculation the slope between the origin and each of the points.
Let
therefore the slope is,
Now let,
thus the slope is,
From here set the slopes equal to each other and solve for k.
Multiply by k on both sides.
Example Question #126 : Coordinate Geometry
Figure NOT drawn to scale
On the coordinate axes shown above, the shaded triangle has area 60.
Give the slope of the line that includes the hypotenuse of the triangle.
The length of the vertical leg of the triangle is the distance from the origin 
The area of a right triangle is half the product of the lengths of its legs 
Since this is the positive horizontal distance from the origin, this is also the 
The slope of a line, given the intercepts 
Substitute 
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