When it is easier to use the point-slope form to write the equation of a line and when it is easier to use the slope-intercept form?

Point slope form is used when we have the information of at least two coordinates that lie on the line

For example:

Given that coordinate (3, 4) and (6, 7) lies on a straight line. 

We work out the equation of the line by substituting the two coordinates into the formula (y - y₁) = m(x - x₁) where (x₁, y₁) could be either (3, 4) and (6, 7).

We would need to use both coordinates to work out the gradient (m) by using the formula:

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The slope intercept form is used when we are given enough information to work out the gradient as well as the y-intercept. 

For example:
Given two coordinates (3, 5) and (0, 9)
This information can help to find the gradient and the y-intercept.
The y-intercept would be at 9 because the (0, 9)
We calculate the gradient m
Then substitute into y=mx+c which is the slope intercept form.