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).
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.
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10 common questions about slope
1. Is slope also called gradient?
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.
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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