Question

Why is the equation y-y1=m(x-x1) called the point-slope form?

Answer 1

The equation of the line with slope m = 2 and passing through the point (1, 1) will be:

`y = 2x`

Explanation:

We know that the point-slope form of the line equation is

`y-y_1=m\left(x-x_1\right)`

where

• m is the slope of the line

• (x₁, y₁) is the point

The formula
`y-y_1=m\left(x-x_1\right)` is termed as the point-slope form of the line equation because if we know one point on a certain line and the slope of that line, then we can easily get the line equation with this formula and, hence, determine all other points on the line.

For example, if we are given the point (1, 1) and slope m = 2

Then substituting the values m = 2 and the point (1, 2)

`y-y_1=m\left(x-x_1\right)`

`y - 2 = 2(x-1)`

`y - 2 = 2x-2`

`y = 2x-2+2`

`y = 2x`

Therefore, the equation of the line with slope m = 2 and passing through the point (1, 1) will be:

`y = 2x`