### All PSAT Math Resources

## Example Questions

### Example Question #1 : 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

–9

11

–10

**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 #2 : Lines

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

**Possible Answers:**

3/2

5/7

2

2/3

**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 #3 : Lines

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

**Possible Answers:**

–2/5

2/3

-3/5

–2/3

2/5

**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 #4 : Lines

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

**Possible Answers:**

*y* = *x*√3 + 2

*y* = *x*

*y* = *x*√2 - 2

*y* = *x* - √2

*y* = *x*((√3)/3) + 1

**Correct answer:**

*y* = *x*√3 + 2

### Example Question #5 : Lines

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 #6 : Lines

What is the slope between and ?

**Possible Answers:**

**Correct answer:**

Let and

so the slope becomes .

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

**Possible Answers:**

**Correct answer:**

### Example Question #8 : Lines

Refer to above red line. What is its slope?

**Possible Answers:**

**Correct answer:**

The slope of a line. given two points can be calculated using the slope formula

Set :

### Example Question #9 : Lines

Which of the following equations has as its graph a line with slope 4?

**Possible Answers:**

None of the other responses is correct.

**Correct answer:**

For each equation, solve for and express in the slope-intercept form . The coefficient of will be the slope.

Slope:

Slope:

Slope:

Slope: .

The line of the equation

is the one with slope 4.

### Example Question #10 : Lines

Solve the equation for *x* and *y*.

–*x* – 4*y* = 245

5*x* + 2*y* = 150

**Possible Answers:**

*x *= 234/5

*y *= 1245/15

*x *= 545/9

*y* = –1375/18

*x* = 3

*y* = 7

*x *= –1375/9

*y *= 545/18

**Correct answer:**

*x *= 545/9

*y* = –1375/18

While solving the problem requires the same method as the ones above, this is one is more complicated because of the more complex given equations. Start of by deriving a substitute for one of the unknowns. From the second equation we can derive y=75-(5x/2). Since 2y = 150 -5x, we divide both sides by two and find our substitution for y. Then we enter this into the first equation. We now have –x-4(75-(5x/2))=245. Distribute the 4. So we get –x – 300 + 10x = 245. So 9x =545, and x=545/9. Use this value for x and solve for y. The graph below illustrates the solution.

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