Slope-Intercept form of a Line

A straight line’s slope intercept form is the most frequent way to show 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 of the points on that line should satisfy the line condition. 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

A method for knowing the equation of a straight line in the  plane is the slope intercept form method. A straight line’s equation is the relationship that:

• The coordinates of any place on the line must intersect.
• Any point that is not on the line’s coordinates is unsatisfactory.

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.

Slope Intercept form:

The equation of a line is found using the slope-intercept form of a straight line. We need to know the slope of the line and the intercept cut by the line with the y-axis to use 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 form Example:

Here are some examples of the slope intercept form.

• The equation for a line with a slope of -1 and a y-intercept of (4) is y = -x + 4.
• y = 2x is the equation for a line with slope (2) and passing through the origin (y-intercept = 0).

Note: tanθ can be used to compute the slope of the line for which the angle of inclination θ is given. Also, in the situation of two points on a straight line (x1, y1) and (x2, y2), the slope can be expressed as (y2 – y1)/ (x2 – x1).

Slope Intercept Formula:

Given the required parameters, the slope-intercept formula is used to compute the slope, y-intercept, x-intercept, or equation of a straight line. When we know the slope of a straight line, which is denoted by m, and the y-intercept of a straight line, which is denoted by b or c, we may use the slope-intercept formula.

Slope Intercept Formula in Mathematics:

The equation of the line, using the slope-intercept formula, is:

y = mx + b 

where,

m = the line’s slope; 

b = the line’s y-intercept

(x, y) represent each point on the line, and x and y must be used as variables in the above expression.

Example:

1] A line’s equation is 3x + 4y + 5 = 0. Using the slope intercept form, find the line’s slope and y-intercept.

Solution: The equation of the line is rearranged to the conventional form y = mx + b.

We have:

4y = -3x – 5 

⇒ y = (-3/4)x + (-5/4)

Thus, m = -3/4 , b = -5/4.

Straight line equation using slope intercept form:

To find the equation of a line with an arbitrary inclination, we’ll need two numbers: the line’s inclination (also known as its slope or angle with the x-axis) and its location. These two properties can be used to identify the uniqueness of any line.

The steps for determining a line’s equation using the slope-intercept form are listed below.

Step 1: Write down the y-intercept, ‘b,’ and the line’s slope,’m.’ If the slope of a straight line is not given explicitly and other necessary data is provided, we can use the slope formula to find it.

Step 2: Write y = mx + b in the slope intercept formula.

Conclusion:

y=mx+b is the slope intercept form, where m is the slope and b is the y-intercept. The graph of a linear equation can be drawn using this version of the equation. A straight line’s slope intercept form is the most frequent way to show 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. 

A method for knowing the equation of a straight line in the  plane is the slope intercept form method. The equation of a line is found using the slope-intercept form of a straight line. We need to know the slope of the line and the intercept cut by the line with the y-axis to use the slope-intercept formula.

Given the required parameters, the slope-intercept formula is used to compute the slope, y-intercept, x-intercept, or equation of a straight line. To find the equation of a line with an arbitrary inclination, we’ll need two numbers: the line’s inclination (also known as its slope or angle with the x-axis) and its location.