Algebra 1 : Functions and Lines

Study concepts, example questions & explanations for Algebra 1

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Example Questions

Example Question #2 : How To Find Out If A Point Is On A Line With An Equation

Which of the following ordered pairs lies on the line given by the equation ?

Possible Answers:

Correct answer:

Explanation:

To determine which ordered pair satisfies the equation, it would help to rearrange the equation to slope-intercept form.

Then, plug in each ordered pair and see if it satisfies the equation. We are looking for an value that produces the desired answer.

 satisfies the equation. All of the other points do not.  

(Note: you could also use the original equation in standard form).

Example Question #1 : How To Find Out If A Point Is On A Line With An Equation

The point (3,2) is located on which of these lines?

Possible Answers:

Correct answer:

Explanation:

To determine whether a point is on a line, you can plug it into the equation to see if the equation remains valid/equal with the point.

Plugging the point (3,2) into the equation gives you

which works out. None of the other equations would remain equal after pluggin in (3,2).

Example Question #1 : How To Find Out If A Point Is On A Line With An Equation

The point (2,7) lies on which of these lines?

Possible Answers:

None of these answers

Correct answer:

Explanation:

To determine whether a point is located in a given line, simply plug in the coordinates of the point into the line. In this case, plugging in the coordinates into the only line where you can plug in the coordinates and have a valid equation is . Plugging in (2,7) would give you an equation of , which works out to .

Example Question #2 : How To Find Out If A Point Is On A Line With An Equation

Which of these points fall on the graph of the line 

Possible Answers:

Two of these points fall on the graph of this equation.

All three of these points fall on the graph of this equation.

Correct answer:

All three of these points fall on the graph of this equation.

Explanation:

To find out if a point is on a line with an equation, we just need to substitute in the point's  and  values and see if the equation holds true. For example, let's look at the point . Substitution into the equation gives us 

or 

, which is true.

So, this point does fall on the line. Doing the same with the other two points shows us that yes, all three of them fall on the line expressed by this equation.

Example Question #1 : How To Find Out If A Point Is On A Line With An Equation

Which point is on the line 

Possible Answers:

Correct answer:

Explanation:

To determine if a point is on a line you can simply subsitute the x and y coordinates into the equation. Another way to solve the problem would be to graph the line and see if it falls on the line. Plugging in  will give  which is a true statement, so it is on the line.

Example Question #11 : How To Find Out If A Point Is On A Line With An Equation

Which of these coordinate pairs or points lies on the line .

Possible Answers:

Correct answer:

Explanation:

To see if a point is directly on a line, plug that point into the equation replacing the x in the slope intercept equation by the x coordinate and the y with the y coordinate respectively and then simplify. If the equation is a true statement like 1=1 or 5=5 then that coordinate pair is on the line.

Since we ended up with a true statement, the point  indeed is on the line  .

 

Example Question #12 : How To Find Out If A Point Is On A Line With An Equation

Given the equation , which of these points lie on this line?

Possible Answers:

None of these.

Correct answer:

None of these.

Explanation:

To ascertain if a point lies on a line, substitute the coordinate pair into the equation of the line and simplify. If the equation yields a true statement then that point lies on the line.

Unfortunately none of the points lie on our line, but this is how one would find out:

 

Based on the graph of this line it appears (1,1) is on this line. 

Because this statement is not true, (1,1) is not on the line. Try this same method with the rest of the coordinate pairs to see that they do not lie on our line.

Example Question #13 : How To Find Out If A Point Is On A Line With An Equation

Which of the following points belongs on the line  ?

Possible Answers:

Correct answer:

Explanation:

This question asks which of the given points belongs on the line . This is another way of asking which of the points does the line pass through.

This question can be quickly solved for by substituting in the given points. This may also be known as the "plug and chug" method. 

Each point (coordinate) represents an  and a  value through this format: 

Simply by arbitrarily substituting in the  or  into the equation  and solving for  or , you can determine if the point belongs on the line if you are left with the given point. 

For example, using the point that does belong on the line: 

substituting in the  value from , where , into the equation , we can solve for 

 and given that  in the coordinate , we know that this coordinate would belong. 

If we did not receive the anticipated  value from the coordinate, we can automatically deduce that the point does not belong on the line. For example, using  and substituting in the  value, 

Because , we can deduce that  does not belong on the line .

Example Question #14 : How To Find Out If A Point Is On A Line With An Equation

Which of the following points does not belong on the line  ?

Possible Answers:

Correct answer:

Explanation:

This question asks which of the given points does not belong on the line . This is another way of asking which of the points does the line not pass through.

This question can be quickly solved for by substituting in the given points. This may also be known as the "plug and chug" method. But first, let's rewrite the equation in a more comfortable format with a positive . This can be achieved by multiplying  to both sides of the equation so the result will be: 

Each point (coordinate) represents an  and a  value through this format: 

Simply by arbitrarily substituting in the  or  into the equation  and solving for  or , you can determine if the point belongs on the line if you are left with the given point. 

For example, using a point that does belong on the line: 

substituting in the  value from , where , into the equation , we can solve for 

 and given that  in the coordinate , we know that this coordinate would belong. 

If we did not receive the anticipated  value from the coordinate, we can automatically deduce that the point does not belong on the line. For example, using  and substituting in the  value, 

Because , we can deduce that  does not belong on the line .

Example Question #15 : How To Find Out If A Point Is On A Line With An Equation

Which of the following points belongs on the line  ? 

Possible Answers:

Correct answer:

Explanation:

This question asks which of the given points belongs on the line . This is another way of asking which of the points does the line pass through.

This question can be quickly solved for by substituting in the given points. This may also be known as the "plug and chug" method. 

Each point (coordinate) represents an  and a  value through this format: 

Simply by arbitrarily substituting in the  or  into the equation  and solving for  or , you can determine if the point belongs on the line if you are left with the given point. 

For example, using the point that does belong on the line: 

substituting in the  value from , where , into the equation , we can solve for 

 and given that  in the coordinate , we know that this coordinate would belong. 

If we did not receive the anticipated  value from the coordinate, we can automatically deduce that the point does not belong on the line. For example, using  and substituting in the  value, 

Because , we can deduce that  does not belong on the line .

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