### All SAT Math Resources

## Example Questions

### Example Question #101 : Coordinate Geometry

Based on the table below, when x = 5, y will equal

x |
y |

-1 |
3 |

0 |
1 |

1 |
-1 |

2 |
-3 |

**Possible Answers:**

11

–10

–11

–9

**Correct answer:**

–9

Use 2 points from the chart to find the equation of the line.

Example: (–1, 3) and (1, –1)

Using the formula for the slope, we find the slope to be –2. Putting that into our equation for a line we get y = –2x + b. Plug in one of the points for x and y into this equation in order to find b. b = 1.

The equation then will be: y = –2x + 1.

Plug in 5 for x in order to find y.

y = –2(5) + 1

y = –9

### Example Question #1 : Slope And Line Equations

What is the slope of a line that runs through points: (-2, 5) and (1, 7)?

**Possible Answers:**

2/3

5/7

3/2

2

**Correct answer:**

2/3

The slope of a line is defined as a change in the y coordinates over a change in the x coordinates (rise over run).

To calculate the slope of a line, use the following formula:

### Example Question #1 : Slope And Line Equations

A line passes through the points (–3, 5) and (2, 3). What is the slope of this line?

**Possible Answers:**

2/3

2/5

-3/5

–2/5

–2/3

**Correct answer:**

–2/5

The slope of the line that passes these two points are simply ∆y/∆x = (3-5)/(2+3) = -2/5

### Example Question #1 : Geometry

Which of the following lines intersects the *y*-axis at a thirty degree angle?

**Possible Answers:**

*y* = *x*√2 - 2

*y* = *x*

*y* = *x* - √2

*y* = *x*((√3)/3) + 1

*y* = *x*√3 + 2

**Correct answer:**

*y* = *x*√3 + 2

### Example Question #1 : Geometry

What is a possible slope of line *y*?

**Possible Answers:**

–2

2

**Correct answer:**

–2

The slope is negative as it starts in quadrant 2 and ends in quadrant 4. Slope is equivlent to the change in *y* divided by the change in *x*. The change in *y* is greater than the change in *x*, which implies that the slope must be less than –1, leaving –2 as the only possible solution.

### Example Question #1 : Geometry

What is the slope between and ?

**Possible Answers:**

**Correct answer:**

Let and

so the slope becomes .

### Example Question #1 : How To Find The Slope Of A Line

What is the slope of line 3 = 8y - 4x?

**Possible Answers:**

-0.5

2

-2

0.5

**Correct answer:**

0.5

Solve equation for y. y=mx+b, where m is the slope

### Example Question #2 : How To Find The Slope Of A Line

Find the slope of the line 6X – 2Y = 14

**Possible Answers:**

12

3

-6

-3

**Correct answer:**

3

Put the equation in slope-intercept form:

y = mx + c

-2y = -6x +14

y = 3x – 7

The slope of the line is represented by M; therefore the slope of the line is 3.

### Example Question #1 : How To Find The Slope Of A Line

If 2x – 4y = 10, what is the slope of the line?

**Possible Answers:**

0.5

–0.5

2

–5/2

–2

**Correct answer:**

0.5

First put the equation into slope-intercept form, solving for y: 2x – 4y = 10 → –4y = –2x + 10 → y = 1/2*x – 5/2. So the slope is 1/2.

### Example Question #31 : Coordinate Geometry

What is the slope of the line with equation 4*x* – 16*y* = 24?

**Possible Answers:**

1/8

–1/4

1/2

–1/8

1/4

**Correct answer:**

1/4

The equation of a line is:

*y* = *mx* + *b*, where *m* is the slope

4*x* – 16*y* = 24

–16*y* = –4*x* + 24

*y* = (–4*x*)/(–16) + 24/(–16)

*y* = (1/4)*x* – 1.5

Slope = 1/4

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