y=-3/4x+3

I found this by visualising a triangle made up of the x-axis, y-axis, and the 5 unit segment that connects from the x-intercept to the y-intercept. Because this must be a right triangle, you can use the pythagorian theorum to find the left side(y-axis) which is 3 units. The line that connects (0,3) to (4,0) is y=-3/4x+3.

Next, the slope of the new line must be 4/3 (opposite of reciprocal). Now using the newfound slope create a linear equation and sub in the original point (1/4,5):

(5)=4/3(1/4)+b

In solving for b, we get:

(5)=4/12+b

b=14/3

thus:

y=(4/3)x+14/3

or

4x-3y=-14

Note: the distance formula can probably be used in place of the pythagorean theorum.

—-edit—-

fixed mistake, I mixed up the 4 and 5, not intentionally.

Again, use the general formula for a linear function:

y = mx + b

m is slope and b is y-intercept.

Find the y-intercept of the perpendicular line.

It helps to envision a triangle, including the x-axis, y-axis and a line connecting the x- and y-intercepts.

The bottom leg of this triangle is 4, since that’s the x-intercept. The hypotenuse of this triangle is 5 (given in the problem statement). Now, use the Pythagorean theorem to find the length of the upright leg, which will give you the y-intercept. You’ll get 3.

Thus, the y-intercept is (0,3).

Now, you need to find the equation of the perpendicular line. You already know b: it’s 3, according to the general formula for a linear function.

Now, plug in the x-intercept point, along with the value for b, to find the slope:

y = mx + b

0 = m(4) + 3

4m = -3 or m = -3/4

Next idea: perpendicular lines have slopes that are negative inverses of each other. That is, if one line has the slope m, then the other line has the slope -1/m.

So, the slope of the line you’re looking for is the negative inverse of -3/4, which is 4/3.

Plug in the point you’re given on your line to find the value of b (you know that m = 4/3):

5 = (4/3)*(1/4) + b

5 = 1/3 + b

b = 14/3

So, your equation is y = (4/3)x + 14/3.

The guy above has the right reasoning, but he messed up the interpretation of your statement. He assumed that the y-intercept was (0,5), but you say that it’s 5 units away from the x-intercept. That means 5 should be the hypotenuse of the triangle he visualized.

http://www.math-videos-online.com/free-math-homework-help.html