### All ISEE Middle Level Quantitative Resources

## Example Questions

### Example Question #1 : Geometry

Give the equation of the line through point that has slope .

**Possible Answers:**

**Correct answer:**

Use the point-slope formula with

### Example Question #1 : Geometry

Which is the greater quantity?

(A) The slope of the line

(B) The slope of the line

**Possible Answers:**

It is impossible to determine which is greater from the information given

(A) and (B) are equal

(B) is greater

(A) is greater

**Correct answer:**

(A) is greater

Rewrite each in the slope-intercept form, ; will be the slope.

The slope of this line is .

The slope of this line is .

Since , (A) is greater.

### Example Question #1 : Coordinate Geometry

Which is the greater quantity?

(A) The slope of the line

(B) The slope of the line

**Possible Answers:**

It is impossible to determine which is greater from the information given

(A) is greater

(A) and (B) are equal

(B) is greater

**Correct answer:**

(A) and (B) are equal

Rewrite each in the slope-intercept form, ; will be the slope.

The slope of the line of is

The slope of the line of is also

The slopes are equal.

### Example Question #3 : Geometry

and are positive integers, and . Which is the greater quantity?

(a) The slope of the line on the coordinate plane through the points and .

(b) The slope of the line on the coordinate plane through the points and .

**Possible Answers:**

It is impossible to determine which is greater from the information given

(a) is the greater quantity

(a) and (b) are equal

(b) is the greater quantity

**Correct answer:**

(a) and (b) are equal

The slope of a line through the points and can be found by setting

in the slope formula:

The slope of a line through the points and can be found similarly:

The lines have the same slope.

### Example Question #2 : Coordinate Geometry

A line passes through the points with coordinates and , where . Which expression is equal to the slope of the line?

**Possible Answers:**

Undefined

**Correct answer:**

The slope of a line through the points and , can be found by setting

:

in the slope formula: