About Slope Intercept Form
A straight line's slope intercept form is one of the most frequent ways to represent the equation of a line. When given the slope of a straight line and the y-intercept, the slope intercept formula can be used to derive the equation of a line ( the y-coordinate of the point where the line intersects the y-axis). The equation of a line is the equation that each point on that line must satisfy. There are several ways to find this straight line equation, which is written as,
- Slope-intercept form
- Point slope form
- Two-point form
- Intercept form
What do you mean by Slope Intercept Form of a Straight Line?
A method for determining the equation of a straight line in the coordinate plane is the slope intercept form. A straight line's equation is the relationship that:
- Any point on the line's coordinates must satisfy.
- Any point not on the line's coordinates will not satisfy.
The solution to this problem is obvious. We'll need the slope, or angle of inclination, of this straight line from the x-axis and the intercept it makes with the y-axis to obtain the slope intercept form of a straight line.
Definition of Slope Intercept Form
The equation of a line is found using the slope-intercept form of a straight line. The slope of the line and the intercept cut by the line with the y-axis are required for the slope-intercept formula. Consider a straight line with the slope'm' and the y-intercept 'b.' y = mx + b is the slope intercept form equation for a straight line with a slope,'m,' and 'b' as the y-intercept.
Slope Intercept Formula
The equation of the line, using the slope-intercept formula, is:
y = mx + b
Here, m is slope of line, b is y-intercept of line, (x, y) represent every point on line,x and y have to be kept as the variables while applying the above formula.
The slope-intercept formula cannot be used to determine a vertical line's equation.
Example: A line's equation is 3x + 4y + 5 = 0. Using the slope intercept form, find the line's slope and y-intercept.
Sol: The equation of the line is rearranged to the conventional form y = mx + b.
4y = -3x - 5
⇒ y = (-3/4)x + (-5/4)
Thus, m = -3/4 , b = -5/4
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