Find an equation of the line in the form axbyc where ab and

Find an equation of the line in the form ax+by=c, where a,b, and c, are intergers with no facotor common to all three and a >0. The line with y-intercept 9 and perpendicular to x+4y=7 is

Solution

Answer

We have to find an equation of line aX + bY = c

Condition that,   

Clearly, the first thing we need to do is solve \" X + 4Y = 7\" for \"Y=\", so that we can find our reference slope:

X + 4Y = 7

4Y = 7 – X

Y = (-1/4)X + (7/4)

So the reference slope from the reference line is m = - ¹/₄

For the perpendicular line, we have to find the perpendicular slope. The reference slope is m = -¹/₄, and, for the perpendicular slope, we’ll flip this slope and change the sign.

Then the perpendicular slope is m = 4. and this line is passing through (0,9)

Y – 9 = 4 (X – 0)

Y = 4X + 9

Converting it in desired equation form

4X – Y = - 9

Therefore,

a = 4,        b = -1 and        c = -9