Graph work delemma?

Question

Find the equation of the line through (1, 4) with slope ¼. Write the answer in slope-intercept form

My Answer:
y=m(x-k)+h

y= ¼ (x-1) + 4

Slope intercept
y= 1/4x –1/4 + 4 = 1/4x + 15/4

teacher comment:Great, except 1/4x means 1 divided by 4x and that is incorrect. Minus 1.
Minus 1 for no solution checks. You must check at least the given point.

Solution Check?

Answer 1

The teacher is right; write it as x/4 or (1/4)x

Answer 2

You have come up with the correct solution, now lets check if it is correct. First, get a piece of graph paper and make a point at x=1 and y=4. You know your line goes though that point. The slope is 1/4. Slope is rise over run, which means that for every four units you increase x, y will go up 1 unit. Start at (1,4) add 4 to x and 1 to y and plot the point (5,5). Do this again and plot (9,6). Draw your line through these points. Now check to see if your equation works. If it does, when you plug in x=1, you should get y=4 (since 1,4 is on your graph). Put in x=5 you should get y=5, for x=9 y should be 6. When x=1, y=1/4(1)+15/4=16/4=4 . Right so far. When x=5, y=1/4(5)+15/4=20/4=5. Right again. When x=9, y=1/4(9)+15/4=24/4=6. Right. So your equation is correct. If you have drawn your graph accurately, you can check your formula for any x value, and the y value on the graph should be the same as your calculated value.

Answer 3

Let's see:

"1/4x means 1 divided by 4x and that is incorrect"

Nope, your teacher is wrong here. Order of operations states that multiplications and divisions have equal priority and are evaluated in order from left to right. Ergo, 1/4x means one fourth times x. See, for instance http://mathforum.org/library/drmath/view/57222.html . Your original answer was correct as written.

"Minus 1 for no solution checks"

Solution checks refers to some test performed in order to make sure that the solution makes sense. For instance, when solving a system of equations, you would substitute the obtained values for x and y into the equations to see whether you really do obtain an equality. In this case, solution checks would mean substituting the x and y-coordinates of the original point into the equation in order to see whether the point is on the line. However, it's really unnecessary here, considering that the point-slope form ALWAYS yields a point on the line, and you only did one algebraic manipulation on it to get the final equation, which is probably harder to screw up than the solution check. Since the question does not actually state that you have to check the solution, I think that it was absurd to mark you down for not doing so. Of course, if your teacher has elsewhere stated that all solutions must be checked, she's within her rights, but I'd still dock her several points for making her students do unnecessary work.

Answer 4

I'm a math teacher, and probably would not have taken off for the 1/4x, but you should be very careful with that.

1
-- x
4

would also have worked provided you write it clearly.

Good point with the check though. You should always check your solutions.

Answer 5

(1,4), m = (1/4)

4 = (1/4)(1) + b
4 = (1/4) + b
16 = 1 + 4b
4b = 15
b = (15/4)

ANS : y = (1/4)x + (15/4)

What she means is, because you didn't put it as (1/4)x, you had it incorrect. 1/4x without the (1/4)x, would be understood as (1/(4x)) instead of what is meant.

Answer 6

ur teacher was right.
the answer should be y = (1/4)x + 15/4
or = x/4 + 15/4

Answer 7

that is the solution it says find the equation