# ACT Math : How to find the slope of a line

## Example Questions

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### Example Question #11 : How To Find The Slope Of A Line

What is the slope of the line perpendicular to ?

Explanation:

To begin, it is easiest to find the slope of a line by putting it into the form .   is the slope, so you can immediately find this once you have the format correct.  Thus, solve our equation for :

Now, recall that perpendicular lines have slopes of opposite sign and reciprocal numerical value.  Thus, if our slope is , its perpendicular paired line will have a slope of .

### Example Question #12 : How To Find The Slope Of A Line

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

Explanation:

The easiest way to find the slope of a line based on its equation is to put it into the form . In this form, you know that  is the slope.

Now, subtract  from both sides:

Next, subtract  from both sides:

Finally, divide by :

This is the same as:

Thus, the slope is .

### Example Question #13 : How To Find The Slope Of A Line

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

Explanation:

The slope of an equation can be calculated by simplifying the equation to the slope-intercept form , where m=slope.

Since , we can solve for y. In shifting the 5 to the other side, we are left with .

This can be further simplified to

, leaving us with the slope intercept form.

In this scenario, , so slope .

### Example Question #9 : How To Find The Slope Of A Line

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

-6

3

12

-3

3

Explanation:

Put the equation in slope-intercept form:

y = mx + b

-2y = -6x +14

y = 3x – 7

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

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