How to find slope of straight line

How to find slope of straight line: The slope of a line is a measure of the incline of the line. A positive slope indicates a line that goes UP from left to right. This line has a positive slope.

A negative slope indicates that a line goes DOWN if you are moving from left to right. This line has a negative slope.

Why slope of a line?

Knowing the value for the slope of a line is necessary when writing its equation. And also, the slope of a line indicates how to step the line is.

So, knowing how to find the slope of a line is an important skill for higher Geometry and Algebra concepts.

How to find the slope of a line?

There are two common ways to find the slope of a line.

• 1. Slope-intercept method (Using the general equation of a straight line, y = mx + c)
• 2. Using the two-points method.

Method 1: Slope-intercept method

To change an equation to slope-intercept form, make y the subject of the equation so that the equation is in the form y = mx + c.

Follow these two steps:

Step 1: Solve the equation for y (i.e. make y the subject)

Step 2: The variable in front of the x (referred to as m) is the slope.

Example: Find the slope of the line 2x + y − 2 = 0.

Step 1: Solve the equation 2x + y − 2 = 0 for y.

• 2x + y − 2 = 0 for y.(Subtract 2x from both sides of the equation)
• y − 2 = −2 x (Add 2 to both sides of the equation)
• y = −2x + 2 (Now, this is in the form y = mx + c)

Step 2: The number in front of x is the slope.

• −2 is in front of x, so −2 is the slope.

Quick hits #1: Change each of the following equations to slope-intercept form and find the slope.
1. 5x − y + 2 = 0
2. 4x + 2y = −8
3. 7y = −3x
4. x + 2y = 1

The answers are at the end of this article.

Method 2: Two-points method (find slope between two points)

To find the slope of a line using the point-point method, just find two points on the line.

Step 1: Find two points on the line.

Step 2: Find the change in y: Subtract the first y-coordinate (y₁) from the second y-coordinate (y₂).
y₂ – y₁
Step 3: Find the change in x: Subtract the first x-coordinate ( x₁) from the second x-coordinate ( x₂).
x₂ -x₁
Step 4: Divide the change in y (Step 2) by the change in x (Step 3). The answer is the slope of the line.
Slope = (y₂ – y₁)/ ( x₂ -x₁)

Example: Find the slope of a line through the points (3, 2) and (7, 1).

• 1: Find two points on the line. Two points on the line are given (3, 2) and (7, 1).
• 2: Find the change in y 2. − 1 = 1
• 3: Find the change in x 3. − 7 = −4
• 4: Find the slope of the line by dividing the change in y (Step 2) by the change in x (Step 3).
  ¹/₍₋₄₎ = ^{− 1}/ ₄. The slope is ^{− 1}/ ₄

Quick hits#2: Find the slope of the line through the following points.

1. (3, 0) and (0, −2)
2. (7, 1) and (2, 6)
3. (0, 0) and (5, 3)
4. (−3, −2) and (1, 1)

The answers are at the end of this article.

Check out our free maths worksheets here and download them. If you have a question, leave a comment and we will get back to you.

10 common questions about slope

1. Is slope also called gradient?
A. Yes

2. What is the slope of a straight line?
A. The slope of a line is a measure of the incline of the line.

3. What is the slope of a line formula?
A. The formula of a slope is given the ‘change is y’ (the RISE) divide by ‘change is x’ (the RUN).
Slope = ^{RISE (change in y)}/_{RUN (change in x)} 

4. What is the slope of the line parallel to the x-axis?
A. Slope = 0.
There is no (zero) rise. Slope = 0/_RUN = 0

5. What is the slope of the line parallel to the y-axis?
A. No slope.
(The slope is undefined. Slope = ^RISE/_RUN  = ^RISE/0  = undefined)

6. What is the slope of a horizontal (flat) line?
A. Slope = 0
A flat line is also called the line parallel to x-axis.

7. What is the slope of a vertical line?
A. No slope
A vertical line is also called ‘the line parallel to the x-axis.

8. How can I find the slope of a straight line?
A. There are two ways of finding the slope of a straight line: By using the slope-intercept form, y = mx + c; or the Two-points method.

9. How can I identify slope in the equation y = mx + c?
A. m in the equation represents the slope.

10. How to find the slope of a line with two points?
A. Use the point-point method to work out the slope of a line given two points.

Free Online Mathematics Worksheets

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Quick hits #1 Answers
1. y = 5x + 2, slope = 5
2. y = −2x − 4, slope = −2
3.y = − 3 7 x, slope = − 3
4. y = −¹/₂ x + ¹/₂ , slope = 1 2

Quick hits #2 Answers
1.  ²/₃     2. −1     3. ³/₅     4. ³/₄