## Example Questions

### Example Question #57 : Graphing

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

7

5

10

12

None of the answers are correct

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?       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 #61 : Graphing

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

3π

0.5

π

2π

1

Explanation:

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

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

What is the midpoint between and ?   None of the answers are correct  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 #1 : How To Graph A Line

If the graph has an equation of , what is the value of ?       Explanation: is the -intercept and equals  can be solved for by substituting in the equation for , which yields  ### Example Question #22 : Graphing

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

III

IV

Cannot be determined

I

II

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 #1 : Graphing Linear Functions 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.      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 #1 : How To Graph A Line Refer to the above diagram. If the red line passes through the point , what is the value of ?      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 :   ### All ACT Math Resources 