ACT Math : How to graph a line

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : How To Graph A Line

What is the distance between (7, 13) and (1, 5)?

 

Possible Answers:

7

5

10

None of the answers are correct

12

Correct answer:

10

Explanation:

The distance formula is given by d = square root [(x2 – x1)2 + (y2 – y1)2].  Let point 2 be (7,13) and point 1 be (1,5).  Substitute the values and solve.

Example Question #1 : How To Graph A Line

What is the slope of this line?Screen_shot_2013-07-13_at_5.10.26_pm

Possible Answers:

Correct answer:

Explanation:

The slope is found using the formula .

We know that the line contains the points (3,0) and (0,6). Using these points in the above equation allows us to calculate the slope.

Example Question #2 : How To Graph A Line

What is the amplitude of the function if the marks on the y-axis are 1 and -1, respectively?

Screen_shot_2013-07-16_at_10.04.45_am

Possible Answers:

1

0.5

2π

3π

π

Correct answer:

1

Explanation:

The amplitude is half the measure from a trough to a peak.

Example Question #3 : How To Graph A Line

What is the midpoint between  and ?

Possible Answers:

None of the answers are correct

Correct answer:

Explanation:

The x-coordinate for the midpoint is given by taking the arithmetic average (mean) of the x-coordinates of the two end points. So the x-coordinate of the midpoint is given by 

The same procedure is used for the y-coordinates. So the y-coordinate of the midpoint is given by 

Thus the midpoint is given by the ordered pair 

Example Question #4 : How To Graph A Line

If the graph has an equation of , what is the value of ?Screen_shot_2013-07-16_at_9.41.58_am

Possible Answers:

Correct answer:

Explanation:

 is the -intercept and equals  can be solved for by substituting  in the equation for , which yields 

Example Question #2 : Graphing

The equation  represents a line.  This line does NOT pass through which of the four quadrants?

Possible Answers:

I

II

IV

III

Cannot be determined

Correct answer:

III

Explanation:

Plug in  for  to find a point on the line:

Thus,  is a point on the line.

Plug in   for  to find a second point on the line:

 is another point on the line.

Now we know that the line passes through the points  and .  

A quick sketch of the two points reveals that the line passes through all but the third quadrant.

Example Question #5 : How To Graph A Line

Line

Refer to the above red line. A line is drawn perpendicular to that line, and with the same -intercept.  Give the equation of that line in slope-intercept form.

Possible Answers:

Correct answer:

Explanation:

First, we need to find the slope of the above line. 

The slope of a line. given two points  can be calculated using the slope formula

Set :

 

The slope of a line perpendicular to it has as its slope the opposite of the reciprocal of 2, which would be . Since we want this line to have the same -intercept as the first line, which is the point , we can substitute  and  in the slope-intercept form:

Example Question #2 : Graphing Functions

Axes

Refer to the above diagram. If the red line passes through the point , what is the value of ?

Possible Answers:

Correct answer:

Explanation:

One way to answer this is to first find the equation of the line. 

The slope of a line. given two points  can be calculated using the slope formula

Set :

The line has slope 3 and -intercept , so we can substitute  in the slope-intercept form:

Now substitute 4 for  and  for  and solve for :

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