Intermediate Geometry : Lines

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

Example Question #121 : Lines

Find the equation of the line that passes through the points  and .

Possible Answers:

Correct answer:

Explanation:

Recall that the slope-intercept form of a line:

,

where  and .

First, find the slope of the line by using the following formula:

Next, find the y-intercept of the line by plugging in  of the points into the semi-completed formula.

Plugging in  yields the following:

Solve for .

The equation of the line is then .

 

Example Question #24 : How To Find The Equation Of A Line

Find the equation of the line that passes through the points  and .

Possible Answers:

Correct answer:

Explanation:

Recall that the slope-intercept form of a line:

,

where  and .

First, find the slope of the line by using the following formula:

Next, find the y-intercept of the line by plugging in  of the points into the semi-completed formula.

Plugging in  yields the following:

Solve for .

The equation of the line is then .

 

Example Question #25 : How To Find The Equation Of A Line

Find the equation of the line that passes through the points  and .

Possible Answers:

Correct answer:

Explanation:

Start by finding the slope of the line.

Now, take one of the points and put the equation into point-slope form. Recall the point-slope form of an equation of a line:

, where  is the slope and  is the point.

Now, simplify this equation so that it is in slope-intercept form. Recall the slope-intercept form of an equation of a line:

, where  is the slope and  is the y-intercept.

Example Question #26 : How To Find The Equation Of A Line

Find the equation of a line that passes through the points  and .

Possible Answers:

Correct answer:

Explanation:

Start by finding the slope of the line.

Now, take one of the points and put the equation into point-slope form. Recall the point-slope form of an equation of a line:

, where  is the slope and  is the point.

Now, simplify this equation so that it is in slope-intercept form. Recall the slope-intercept form of an equation of a line:

, where  is the slope and  is the y-intercept.

Example Question #1401 : Intermediate Geometry

Find the equation of the line that passes through the points  and .

Possible Answers:

Correct answer:

Explanation:

Start by finding the slope of the line.

Now, take one of the points and put the equation into point-slope form. Recall the point-slope form of an equation of a line:

, where  is the slope and  is the point.

Now, simplify this equation so that it is in slope-intercept form. Recall the slope-intercept form of an equation of a line:

, where  is the slope and  is the y-intercept.

Example Question #28 : How To Find The Equation Of A Line

Find the equation of the line that passes through the points  and .

Possible Answers:

Correct answer:

Explanation:

Start by finding the slope of the line.

Now, take one of the points and put the equation into point-slope form. Recall the point-slope form of an equation of a line:

, where  is the slope and  is the point.

Now, simplify this equation so that it is in slope-intercept form. Recall the slope-intercept form of an equation of a line:

, where  is the slope and  is the y-intercept.

Example Question #1411 : Intermediate Geometry

Find the equation of the line that passes through the points  and .

Possible Answers:

Correct answer:

Explanation:

Start by finding the slope of the line.

Now, take one of the points and put the equation into point-slope form. Recall the point-slope form of an equation of a line:

, where  is the slope and  is the point.

Now, simplify this equation so that it is in slope-intercept form. Recall the slope-intercept form of an equation of a line:

, where  is the slope and  is the y-intercept.

Example Question #30 : How To Find The Equation Of A Line

Find the equation of the line that passes through the points  and .

Possible Answers:

Correct answer:

Explanation:

Start by finding the slope of the line.

Now, take one of the points and put the equation into point-slope form. Recall the point-slope form of an equation of a line:

, where  is the slope and  is the point.

Now, simplify this equation so that it is in slope-intercept form. Recall the slope-intercept form of an equation of a line:

, where  is the slope and  is the y-intercept.

Example Question #31 : How To Find The Equation Of A Line

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Which inequality is graphed above?

Possible Answers:

Correct answer:

Explanation:

The line that serves as the boundary passes through the points  and  and can easily be seen to be the line of the equation .

The graph of the inequality includes the line itself, as is demonstrated by the fact that it is solid, so the correct choice is either

or 

From the diagram, we see that, for example, the point  (and the rest of the positive -axis) is in the set. Since , this makes the statement  true, so that is the inequality to choose.

Example Question #32 : How To Find The Equation Of A Line

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Refer to the above figures. To the left is the graph of the equation 

What inequality is graphed at right?

Possible Answers:

Correct answer:

Explanation:

As indicated by the solid line, the graph of the inequality at right includes the line of the equation, so the inequality graphed is either  

or 

To determine which one, we can select a test point and substitute its coordinates in either inequality, testing whether it is true for those values. The easiest test point is ; it is not part of the solution region, so we want the inequality that it makes false. Let us select the first inequality:

 makes this inequality false, so the graph of the inequality  is the one that does not include the origin. This is the correct choice. (Note that if we had selected the other inequality, we would have seen that  makes it true; this would have allowed us to draw the same conclusion.)

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