Translating the given equation to intercept form by dividing by 12, we see that it has a y-intercept of (0, 3). Intercept form is x/(x-intercept) + y/(y-intercept) = 1.
X/12 + y/3 = 1
Thus, your problem reduces to finding the slope of the line through (5, 4) and (0, 3).
Slope = ∆y/∆x = (4-3)/(5-0) = 1/5
X + 4y = 12
0 + 4y = 12 (make the substitution)
4y = 12 (simplify)
y = 12/4 (divide both sides by 4)
y = 3
X/12 + y/3 = 1
Thus, your problem reduces to finding the slope of the line through (5, 4) and (0, 3).
Slope = ∆y/∆x = (4-3)/(5-0) = 1/5
Your "linear function" has a slope of 1/5 and a y-intercept of (0, 3).
Another way to determine the y-intercept is to substitute x=0 and solve for y.X + 4y = 12
0 + 4y = 12 (make the substitution)
4y = 12 (simplify)
y = 12/4 (divide both sides by 4)
y = 3