Question

Write an equation in point-slope form for the line that is parallel to y = 3/4x -

3 and passes through point (4,3).

Answer 1

The point-slope form of the equation of the parallel line is y - 3 =
`(3)/(4)` (x - 4)

Explanation:

Parallel lines have the same slopes and different y-intercepts

The slope-intercept form of the linear equation is y = m x + b, where

• m is the slope

• b is the y-intercept

The point-slope form is of the linear equation is y - y1 = m(x - x1), where

• m is the slope

• (x1, y1) are the coordinates of a point lies on the line

∵ The equation of the given line is y =
`(3)/(4)` x - 3

→ Compare it with the first form of the equation above

∴ m =
`(3)/(4)`

∴ The slope of it is
`(3)/(4)`

∵ Parallel lines have the same slopes

∴ The slope of the parallel line is
`(3)/(4)`

∵ The point-slope form is y - y1 = m(x - x1)

→ Substitute the value of the slope in the form of the equation above

∴ y - y1 =
`(3)/(4)` (x - x1)

∵ The line passes through the point (4, 3)

∴ x1 = 4 and y1 = 3

→ Substitute them in the equation above

∴ y - 3 =
`(3)/(4)` (x - 4)

∴ The point-slope form of the equation of the parallel line is

y - 3 =
`(3)/(4)` (x - 4)