All Intermediate Geometry Resources
Example Questions
Example Question #21 : Other Lines
Which of the following points is on the line ?
Start by rewriting the equation into slope-intercept form.
To find which point is on the line, take the -coordinate, and plug it into the given equation to solve for . If the -value matches the -coordinate of the same point, then the point is on the line.
Plugging in into the given equation will give the following:
Thus, is on the line.
Example Question #1371 : Intermediate Geometry
Which of the following points is on the line ?
Start by rewriting the equation into slope-intercept form.
To find which point is on the line, take the -coordinate, and plug it into the given equation to solve for . If the -value matches the -coordinate of the same point, then the point is on the line.
Plugging in into the given equation will give the following:
Thus, is on the line.
Example Question #91 : Coordinate Geometry
Which of the following points is found on the line ?
Start by rewriting the equation into slope-intercept form.
To find which point is on the line, take the -coordinate, and plug it into the given equation to solve for . If the -value matches the -coordinate of the same point, then the point is on the line.
Plugging in into the given equation will give the following:
Thus, is on the line.
Example Question #91 : Coordinate Geometry
True or false:
The line of the equation passes through the point with coordinates .
True
False
False
A line of an equation passes through the point with coordinates if and only if, when , the equation is true. Substitute for and :
- this is false.
The line does not pass through the point.
Example Question #92 : Coordinate Geometry
True or false:
The line of the equation passes through the origin.
True
False
True
The coordinates of the origin are , so the line of an equation passes through this point of and only if is a solution of the equation - or, equivalently, if and only if setting and makes the equation a true statement. Substitute both values:
The statement is true, so the line does pass through the origin.
Example Question #1383 : Intermediate Geometry
True or false:
The lines of the equations
and
intersect at the point .
(Note: You are given that the lines are distinct)
False
True
False
If two distinct lines intersect at the point - that is, if both pass through this point - it follows that is a solution of the equations of both. Therefore, set in the equations and determine whether they are true or not.
Examine the second equation:
False; is not on the line of this equation.
Therefore, the lines cannot intersect at .
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