### All PSAT Math Resources

## Example Questions

### Example Question #1 : How To Find X Or Y Intercept

If the equation of a line is 4*y* – *x* = 48, at what point does that line cross the *x*-axis?

**Possible Answers:**

(0,12)

(0,–12)

(0,–48)

(48,0)

(–48,0)

**Correct answer:**

(–48,0)

When the equation crosses the *x*-axis, *y* = 0. Plug 0 into the equation for *y*, and solve for *x*.

4(0) – *x* = 48, –*x* = 48, *x* = –48

### Example Question #1 : How To Find X Or Y Intercept

Where does the graph of 2x + 3y = 15 cross the x-axis?

**Possible Answers:**

(0,5)

(0,0)

(-7.5,0)

(0,-5)

(7.5,0)

**Correct answer:**

(7.5,0)

To find the x-intercept, set y=0 and solve for x. This gives an answer of x = 7.5.

### Example Question #1 : How To Find X Or Y Intercept

The slope of a line is equal to -3/4. If that line intersects the y-axis at (0,15), at what point does it intersect the x-axis?

**Possible Answers:**

15

20

60

5

-20

**Correct answer:**

20

If the slope of the line m=-3/4, when y=15 and x=0, plug everything into the equation y=mx+b.

Solving for b:

15=(-3/4)*0 + b

b=15

y=-3/4x + 15

To get the x-axis intersect, plug in y=0 and solve for x.

0 = -3/4x + 15

3/4x = 15

3x = 15*4

x = 60/3 = 20

x=20

### Example Question #1 : How To Find X Or Y Intercept

If these three points are on a single line, what is the formula for the line?

(3,3)

(4,7)

(5,11)

**Possible Answers:**

y = 4x - 9

y = 4x + 31

y = 5x + 11

y = 3x - 9

y = 3x - 3

**Correct answer:**

y = 4x - 9

Formula for a line: y = mx + b

First find slope from two of the points: (3,3) and (4,7)

m = slope = (y2 – y1) / x2 – x1) = (7-3) / (4-3) = 4 / 1 = 4

Solve for b by plugging m and one set of coordinates into the formula for a line:

y = mx + b

11 = 4 * 5 + b

11 = 20 + b

b = -9

y = 4x - 9

### Example Question #1 : How To Find X Or Y Intercept

The slope of a line is 5/8 and the x-intercept is 16. Which of these points is on the line?

**Possible Answers:**

(8,15)

(32,10)

(32,30)

(16, 10)

(0,10)

**Correct answer:**

(32,10)

y = mx + b

x intercept is 16 therefore one coordinate is (16,0)

0 = 5/8 * 16 + b

0 = 10 + b

b = -10

y = 5/8 x – 10

if x = 32

y = 5/8 * 32 – 10 = 20 – 10 = 10

Therefore (32,10)

### Example Question #1 : How To Find X Or Y Intercept

A line has the equation: x+y=1.

What is the y-intercept?

**Possible Answers:**

0.5

1

-1

0

2

**Correct answer:**

1

x+y=1 can be rearranged into: y=-x+1. Using the point-slope form, we can see that the y-intercept is 1.

### Example Question #1 : How To Find X Or Y Intercept

A line has the equation: 2x+4y=8.

What is the x-intercept?

**Possible Answers:**

0

8

-4

-8

4

**Correct answer:**

4

To find the x-intercept, rearrange the equation 2x+4y=8 so that x is isolated:

2x=-4y+8

x=-2y+4

Using the point-slope formula, we see that the x-intercept is 4.

### Example Question #1 : How To Find X Or Y Intercept

Given the line 4x + 3y = 12, what is the sum of the x-intercept and the y-intercept?

**Possible Answers:**

3

12

7

1

4

**Correct answer:**

7

Intercepts occur when a line crosses the x-axis or the y-axis. When the line crosses the x-axis, then y = 0 and x = 3. When the line crosses the y-axis, then x = 0 and y = 4. The intercept points are (0, 4) and (3, 0 ). So the y-intercept is 4 and the x intercept is 3 and the sum is 7.

### Example Question #1 : How To Find X Or Y Intercept

What is the y intercept of the following function of x?

y = 3x

**Possible Answers:**

–3

3

1

0

–1

**Correct answer:**

0

The answer is 0 because in slope intercept form, y = mx + b; b is the y intercept. In this case b = 0.

### Example Question #1 : How To Find X Or Y Intercept

What is the x-intercept of a line with a slope of 5 and y-intercept of 3.5?

**Possible Answers:**

(0.7, 0)

(–0.7, 0)

(0, –0.7)

(–3.5, 0)

(3.5, 0)

**Correct answer:**

(–0.7, 0)

To solve this, first find the equation of our line. The form of the question gives it to us very directly. We can use the slope-intercept form (y = mx + b).

y = 5x + 3.5

The x-intercept is found by setting y = 0, because that will give us the x-value at which the line crosses the x-axis.

0 = 5x + 3.5; –3.5 = 5x; x = –3.5 / 5 or –0.7. The point will be (–0.7, 0)

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