Slope Intercept Form
The slope-intercept form is a way to represent a linear equation in algebra
The slope-intercept form is a way to represent a linear equation in algebra. It is written in the form y = mx + b, where m represents the slope of the line and b represents the y-intercept.
In this form, the slope m indicates the rate at which the line is rising or falling as you move from left to right on the coordinate plane. A positive slope means the line is increasing, while a negative slope means the line is decreasing. A slope of zero means the line is horizontal.
The y-intercept b represents the point where the line crosses the y-axis. It is the value of y when x is equal to zero. By knowing the slope m and the y-intercept b, you can easily graph the equation on a coordinate plane.
To convert a linear equation into slope-intercept form, you need to isolate y on one side of the equation. For example, if you have the equation 2x + 3y = 9, you can rearrange it as 3y = -2x + 9 and then divide both sides by 3 to get y = (-2/3)x + 3. In this form, the slope is -2/3 and the y-intercept is 3.
Conversely, if you are given the slope m and the y-intercept b, you can write the equation in slope-intercept form. For example, if you have a slope of 4 and a y-intercept of -2, the equation would be y = 4x – 2.
The slope-intercept form is particularly useful for graphing linear equations and for solving problems related to linear relationships, such as finding the line that best represents a set of data points or determining the equation that represents a certain situation.
I hope this explanation helps you understand the concept of slope-intercept form better. Please let me know if you have any further questions!
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