### All ISEE Lower Level Quantitative Resources

## Example Questions

### Example Question #1 : How To Find A Line On A Coordinate Plane

Which equation of a line is parallel to line segment ?

**Possible Answers:**

**Correct answer:**

In order for the equation to represent a line that is parallel to the line that is shown, the equation must have the same slope as line segment .

Since, line segment has a slope of , the correct equation is:

### Example Question #1 : How To Find A Line On A Coordinate Plane

The points in the above line segment are apart of which of the following linear equations?

**Possible Answers:**

**Correct answer:**

The above line segment is a horizontal line that passes through the axis at Since this line is horizontal, it does not have a slope. Therefore, is the correct answer.

### Example Question #3 : How To Find A Line On A Coordinate Plane

Which of the following linear equations is perpendicular to the line segment shown above?

**Possible Answers:**

**Correct answer:**

Since the line segment is horizontal, the equation that is perpendicular to the segment must run vertically. The only linear equation that runs vertically (perpendicular to ) is .

### Example Question #4 : How To Find A Line On A Coordinate Plane

At what coordinate point does the line intersect with the line segment shown above?

**Possible Answers:**

**Correct answer:**

Since, is perpendicular to the points must cross at , because it is the only coordinate point that both lines pass through.

### Example Question #2 : How To Find A Line On A Coordinate Plane

At which coordinate point does this line segment cross the -axis?

**Possible Answers:**

**Correct answer:**

Keep in mind that the values in the coordinate points are , thus the point is the point at which the line segment passes through the axis.

### Example Question #6 : How To Find A Line On A Coordinate Plane

Find the equation that represents a line that has a intercept of .

**Possible Answers:**

**Correct answer:**

To identify the correct equation, apply the formula , where represents the slope of the line and the intercept.

Thus, the line that passes through the axis at is

### Example Question #3 : How To Find A Line On A Coordinate Plane

Which of the following equations of a line has the steepest slope?

**Possible Answers:**

**Correct answer:**

To find which equation of a line has the steepest slope, apply the formula: , where represents the slope of the line and represents the intercept.

Also, note that , meaning the change in the value, over the change in the value.

The equation that has the largest absolute value of m is the equation that has the steepest slope.

Thus, the equation has the steepest slope, because in order to go from one point to the next move a vertical distance of and a horizontal distance of which is larger than any of the other choices.

### Example Question #31 : Geometry

Find the slope of the line that passes through the coordinate points and .

**Possible Answers:**

**Correct answer:**

To find the slope of the line that passes through these two coordinate points, apply the formula:

Thus the correct answer is:

### Example Question #9 : How To Find A Line On A Coordinate Plane

Line segment has endpoints and . What is the slope of the line segment?

**Possible Answers:**

**Correct answer:**

To find the slope of the line that passes through these two coordinate points, apply the formula:

Thus the correct answer is:

### Example Question #10 : How To Find A Line On A Coordinate Plane

Find the length of the line segment above.

**Possible Answers:**

**Correct answer:**

To find the length of this line segment find the difference between each of the two end points values, since they have the same value.

The difference between and is .

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