### All ACT Math Resources

## Example Questions

### Example Question #1 : How To Graph A Line

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

**Possible Answers:**

12

None of the answers are correct

7

5

10

**Correct answer:**

10

The distance formula is given by d = square root [(x_{2} – x_{1})^{2} + (y_{2} – y_{1})^{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?

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

2*π*

0.5

3*π*

*π*

1

**Correct answer:**

1

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:**

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 ?

**Possible Answers:**

**Correct answer:**

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

### Example Question #5 : How To Graph A Line

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

**Possible Answers:**

IV

II

I

III

Cannot be determined

**Correct answer:**

III

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 #1 : How To Graph A Function

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:**

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 : How To Graph A Function

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

**Possible Answers:**

**Correct answer:**

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 :