Introduction to point slope intercept form

Line equation and slope form:

            A line equation makes the straight line when it is graphed. If the line passes through the points A (x1, y1) and B (x2, y2) and then its slope is,

                        Slope (m) = (y2 - y1)   /  (x2 - x1)

             The slope is defined as the relation between the perpendicular distance and flat distance between any two points. The slope is denoted by letter ‘m’. The slope is also called as the gradient.

Evaluation of Point Slope Intercept Form:

     The slope for the non-linear equation is rate of change varies along the curve; the derivative of the function at a point is the slope of the line tangent to the curve at the point,

                        m = y/x where y and x distances between the two points

            The slope is also calculating the tangent line by m = ‘tan T’

            The point slope equation of a line is,

                        Y = mx + b

            where x and y is the points, m is the slope and b is the y-intercept

Examples for Point Slope Intercept Form:

Ex 1:

            Given point (4, 3) and the slope is 2. Find the equation of this line in point slope intercept form.

Sol:

            Point (4, 3) -> (x1, y1)

            Slope m= 2.

            Equation of the slope point form is

                        y - y1 = m(x - x1)

                        y – 3 = 2(x - 4)

                        y – 3 = 2x - 8 (using distribute property)

                        y – 3 + 3 = 2x – 8 + 3 (Add 3 on both side)

                        y = 2x - 5.

            Slope m = 2. Slope intercept b = -5.

            The line of the equation is y = 2x - 5

Ex 2:

            Given point (4, 3) and (6, 5). Find the equation of this line in point slope intercept form.

Sol:

            Points (4, 3) -> (x1, y1)

            (6, 5) -> (x2, y2)

            To find the equation of line is,

                        y - y1 = m (x - x1)

            Step 1: Take points (4, 3) (6, 5)

                        Slope m = y2 - y1/ x2 - x1

                        M = 5 - 3/6 - 4 -> 2/2 ->1.

            Step 2: Now take slope m = 1 and point (6, 5)

                        y - y1 = m (x - x1)

                        y – 5 = 1(x - 6)

            Step 3: Simplification

                        y – 5 = x - 6 (Using distributive property)

                        y – 5 + 5 = x – 6 + 5 (Add 5 on both side)

                        y = x - 1 .

            Slope m = 1 and Y intercept b = -1

            The line of equation is y = x - 1