Slope-Intercept Form of a Line
In this lesson, we will examine the slope-intercept form of the equation of a line.
About This Lesson
After learning about the slope, x-intercept and y-intercept of a line, it is time for you to learn about the equation of a line that has both the slope and y-intercept (slope-intercept form of a line).
This lesson will show you how the graph of the line will change for different values of slope and y-intercept.
An equation of a line can be written in many forms. Some of these forms are listed below:
- Slope-Intercept Form
- Point-Slope Form
- Two Point Form
An equation of a line can be changed into any of these forms.
Now, watch the following math video to learn more.
Click play to watch video
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Math Video Transcript
In this lesson, we will examine the slope-intercept form of an equation of a line.
The equation of a straight line can be written in the form of y =, m x + b, where m is the slope, and b is the y-intercept.
As for y and x, they are just variables, and can be represented in the graph as y-axis and x-axis respectively.
As you can guess, this equation of a line is in the Slope-Intercept form because it contains both the slope and y-intercept.
Now, to understand more about y = m x + b, let's take a look at this line: y = 2x + 3.
By comparing y = 2x +3 with y = m x +b, we can see that the slope of the line is 2, and the y-intercept is +3.
Now, the line for this equation, y = 2x+3 is shown on the graph.
Since the y-intercept is +3, naturally, this line will cross the y axis at 3.
Alright, when I decrease the y-intercept, notice how the line changes accordingly.
When the y-intercept is changed to +2, note that the line will cross the y-axis at +2.
We will observe a similar behavior when the y-intercept is changed to positive 1, zero, -1, -2, and so on.
Also, notice that, since we are only changing the y-intercept, the slope of the line remains the same.
Next, let's examine the slope, m. When I change the slope, notice how the steepness of the line changes.
As I increases the slope from +2 to +3, we can see that the line becomes steeper.
So, you can see that, the line becomes steeper as the slope continues to increase.
Also, note that, when the slope is positive, the line slants upward to the right.
Next, since we only change the slope, the y-intercept remains same and the line will naturally crosses the y-axis at +1.
Alright, what happens to the line when the slope, m, is zero or negative?
To know this, let us decrease the slope.
Now, see that when the slope is zero, the line becomes parallel to the x-axis.
As the slope becomes negative, the line now slants upward towards the left, and the steepness of the line increases as the slope becomes more negative.
That is all we need to know about y = mx + b for now, we will learn more about in the next lesson.
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