What is the equation in point-slope form of the line passing through (1, 2) and (2, 5)?

Solution:

Point-slope form is used to represent a straight line using its slope and a point on the line.

That means, the equation of a line whose slope is 'm' and which passes through a point (x₁, y₁) is found using the point slope form.

The slope of a line is the change in y coordinate with respect to the change in x coordinate of that line.

The equation of the slope is:

y₂ - y₁ = m (x₂ - x₁)

Where m is the slope of the line

The points given are (1, 2) and (2, 5)

To find the slope

m = (y₂ - y₁)/ (x₂ - x₁)

Substituting the values, we get

m = (5 - 2)/ (2 - 1)

m = 3/1

m = 3

The equation of a line is given by

y = ax + b

To find the real equation, we have to use one point

If we use (1, 2)

2 = a + b

Where a is the slope of the equation

2 = 3 + b

b = 2 - 3

b = -1

y = ax + b

Substituting the values

y = 3x - 1

Therefore, the equation in point-slope form of the line is y = 3x - 1.

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What is the equation in point-slope form of the line passing through (1, 2) and (2, 5)?

Summary:

The equation in point-slope form of the line passing through (1, 2) and (2, 5) is y = 3x - 1.