Point Slope Form Formula

The point-slope form formula is used to represent the point-slope form of the equation of a line. To recall, when the equation of a line using the slope of the line and a point through which the line passes, that equation can be found using the point-slope formula. The steepness of line is a slope (m). The point on the line is in the form of (x1, y1).

The Point Slope Form Formula is,

y – y1 = m (x – x1)

Where,

  • m is the slope of the line
  • x1 is the coordinates of the x-axis
  • y1 is the co-ordinates of the y-axis

Solved Examples

Question 1: Find the equation of a line which passes through the point (2, 6) and has a slope of 7.

Solution:

Given, m = 7

(x1, y1) = (2, 6)

The point slope form formula is,

yy1 = m(xx1)

y – 6 = 7(x – 2)

y – 6 = 7x – 14

7xy – 8 = 0

The equation of the line is: 7xy – 8 = 0

Question 2: Write the point slope equation of a line with slope 5 that passes through the point (3, -2).

Solution:
Given point is (x1, y1) = (3, -2)
Slope = m = 5
Point slope equation is:
y – y1 = m(x – x1)
y – (-2) = 5(x – 3)
This can be further simplified as:
y + 2 = 5x – 15
5x – y – 15 – 2 = 0
5x – y – 17 = 0

Question 3: Find the slope and the point which the equation y – 7 = -3(x – 11) passes through.

Solution:
Given equation of a line is:
y – 7 = -3(x – 11)
Comparing the above equation with y – y1 = m(x – x1)
m = -3
(x1, y1) = (11, 7)
Therefore, slope is -3 and the point is (11, 7).

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