Answer:
Depends on the missing part of the question. See below for a possible answer.
Explanation:
"2x+4y=6 and passes through the point (6,4)" seems to be missing a part of the "question." As written, we are given an equation for a straight line, but it does not pass through point (6.4). It also does not ask a question.
If the problem were preference with something like "What is the equation of a line that is parallel to . ." 2x+4y=6 and passes through the point (6,4), there would be both information and a question. (Another possible scenario is the state the line is perpendicular, not parallel).
Assuming this is the question
Rearrange the given equation into a slope-intercept format of y=mx+b, where m is the slope and b the y-intercept (the value of y when x = 0):
2x+4y=6
4y=-2x+6
y=-(1/2)x+(3/2)
The slope is -(1/2) and the y-intercept is (3/2).
A line parallel to this would have the same slope of -(1/2), so we can write:
y = -(1/2)x + b
Now we need to find a value of b that forces the line through point (6.4). b can be found by using the point in this equation and solving for b:
y = -(1/2)x + b
(4) = -(1/2)(6) + b for (6,4)
(4) = -(3) + b
b = 7
The full equation becomes y = -(1/2)x + 7
See the attached graph.