### All ACT Math Resources

## Example Questions

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

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

**Possible Answers:**

0.5

-0.5

-2

2

**Correct answer:**

0.5

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

### Example Question #113 : Coordinate Geometry

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

**Possible Answers:**

0.5

–5/2

2

–0.5

–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 #114 : Coordinate Geometry

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

**Possible Answers:**

1/4

–1/4

1/8

–1/8

1/2

**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

### Example Question #115 : Coordinate Geometry

What is the slope of a line which passes through coordinates and ?

**Possible Answers:**

**Correct answer:**

Slope is found by dividing the difference in the -coordinates by the difference in the -coordinates.

### Example Question #116 : Coordinate Geometry

What is the slope of the line represented by the equation ?

**Possible Answers:**

**Correct answer:**

To rearrange the equation into a format, you want to isolate the so that it is the sole variable, without a coefficient, on one side of the equation.

First, add to both sides to get .

Then, divide both sides by 6 to get .

If you divide each part of the numerator by 6, you get . This is in a form, and the is equal to , which is reduced down to for the correct answer.

### Example Question #117 : Coordinate Geometry

What is the slope of the given linear equation?

2x + 4y = -7

**Possible Answers:**

1/2

-2

-7/2

-1/2

**Correct answer:**

-1/2

We can convert the given equation into slope-intercept form, y=mx+b, where m is the slope. We get y = (-1/2)x + (-7/2)

### Example Question #118 : Coordinate Geometry

What is the slope of the line:

**Possible Answers:**

**Correct answer:**

First put the question in slope intercept form (y = mx + b):

**–**(1/6)y = **–**(14/3)x **–** 7 =>

y = 6(14/3)x **–** 7

y = 28x **–** 7.

The slope is 28.

### Example Question #119 : Coordinate Geometry

What is the slope of a line that passes though the coordinates and ?

**Possible Answers:**

**Correct answer:**

The slope is equal to the difference between the y-coordinates divided by the difference between the x-coordinates.

Use the give points in this formula to calculate the slope.

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

What is the slope of a line running through points and ?

**Possible Answers:**

**Correct answer:**

The slope is equal to the difference between the y-coordinates divided by the difference between the x-coordinates.

Use the give points in this formula to calculate the slope.

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

What is the slope of the line defined as ?

**Possible Answers:**

**Correct answer:**

To calculate the slope of a line from an equation of the line, the easiest way to proceed is to solve it for . This will put it into the format , making it very easy to find the slope . For our equation, it is:

or

Next you merely need to divide by :

Thus, the slope is

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