a line passes through the point (4,1) and has a slope of 9/4. find the equation of the line.

Answer 1

There are several different "generic" equations that denote a line. The most famous seems to be the slope-intercept form which is y = mx + b. Although you can use this form to solve the problem by inserting the slope 9/4 as "m" and then putting in the point (4, 1) as an ("x", "y") and then solving for "b", an easier way is to use the point-slope form of a line.

Point-Slope form: y - y₁ = m(x - x₁). You know "m" (which is 9/4) and you know (x₁, y₁) which is (4, 1) so plug those in to get:

y - y₁ = m(x - x₁)

y - 1 = 9/4(x - 4)

This is the answer although you can manipulate it a bit to make it look slightly different:

y - 1 = 9/4(x - 4)

y - 1 = 9/4x - 9

y = 9/4x - 8