Point Slope Form Examples

Equation of line using Point Slope Intercept Form:

The equation of a straight line can be derived from its slope and the y-intercept (i.e. point on y axis where line cuts it). For the slope 'm' and y-intercept 'b', the point slope intercept form of a line is given by y = mx + b. This equation can also be obtained from point slope form of a line by substituting the point as (0,b). The example of point slope form is given below.

(i) Find the equation of line having slope 3 and passing through (2,-3):

Using y = mx + b, we have -3 = 3*2 + b => b = -9. hence the equation of line will be y = 3x -9.

Equation for straight line using Point Slope Form of a line:

Having a single point and a slope is enough to find the equation of a straight line. The formula in this case is given by (y – y1) = m (x -x1), where (x1,y1) is a point on line and m is its slope. So let's see some point slope form examples for it.

(ii) Find the equation of line having slope 3 and passing through (2,-3):

Using above equation, (y + 3) = 3 * (x – 2) or y = 3x - 9. Thus we got equivalent solution using both intercept form and line form of the equation.

Examples for Point Slope Form of a linear equation:

Now let's have an example using point slope form of a linear equation.

(iii) Find the equation of line passing through (1,2) and (2,4):

Slope m =(y2-y1)/(x2-x1) = (4-2)/(2-1)=2. Now getting back to the equation, y - 2 = 2(x – 1) or

y=2x which is same as previous one. This equations can also be plotted on a graph by plotting the points and connecting them.

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