write the equation of the line that passes through the point (12,-3) and has a slope of 1/4

Question

Not sure how to write the equation

Answer 1

(12, -3) has a line through it with slope = 1/4 = difference in y coordinates divided by difference in x coordinates

slope = 1/4 =(y- -3)/(x-12) = (y+3)/(x-12)

y+3 = (1/4)(x-12) = x/4 -3

y = x/4 -3-3 = x/4 -6

in slope intercept form, y=mx+b with m=slope=1/4, b= intercept=-6

the equation of the line is y = (1/4)x -6

where the constant term = -6 is the y intercept = (0,-6)

check the answer: plug in the point (12,-3)

x=12, y=-3

y= (1/4)x -6

-3 = (1/4)(12) -6 = 3-6 = -3

or you can eliminate the fraction

4y =x-24

x -4y = 24 in standard form

or x-4y-24=0 in general form, ax+by+c = 0 where a=1, b=-4, c=-24