In the xy-coordinate plane, the slope of line l is 3/4

[supratim7]

In the xy-coordinate plane, the slope of line l is 3/4. Does line l pass through the point (-2/3, 1/2)?

(1) Line l passes through the point (4, 4).
(2) Line l passes through the point (-4, -2).

OA {D}

I figured one doesn't need any calculation for this question.

METHOD-1

stmt 1: "slope" of the line is given (3/4). "x, y values" of a point on the line is given (4, 4)

we can calculate "b"
we can plot the equation of the line in slope-intercept form.
we can check whether (-2/3, 1/2) satisfies this equation.
If (-2/3, 1/2) satisfies, then it must pass through the line.
If (-2/3, 1/2) doesn't satisfy, then it cannot pass through the line. "”» AD

stmt 2: "slope" of the line is given (3/4). x, y values" of a point on the line is given (-4, -2)

same process/logic/soln as stmt (1) "”» D

METHOD-2

stmt 1: "slope" of the line is given (3/4). "x, y values" of a point on the line is given (4, 4). "x, y values" of a point in question is given (-2/3, 1/2)

we can calculate the "slope" that connects these two points.
If the newly calculated "slope" or "m" matches with the given slope (3/4) then both lines must be parallel to each other and since one of the point already belongs to the given line, the other point in question must pass through the given line.
If the newly calculated "slope" or "m" doesn't match with the given slope (3/4) then both lines are not parallel; the other point in question cannot pass through the given line. "”» AD

stmt 2: "slope" of the line is given (3/4). "x, y values" of a point on the line is given (-4, -2). "x, y values" of a point in question is given (-2/3, 1/2)

same process/logic/soln as stmt (1) "”»D

am I on the right track with METHOD 1 & 2? is the reasoning part OK? Hope I am not cutting corners...

Many thanks | Supratim

[RonPurewal]

yep, those are both perfectly valid. nicely done.

[supratim7]

Thank you Ron. Appreciate it :)

[jnelson0612]

:-)