Question

a baker bakes 32 loaves of bread in 4 hours and 54 loaves in 6 hours. write an equation in standard form that represents the linear relationship between the number of hours, x, and the number of loaves, y.\
\\(-12x - y = 11\\)\
\\(12x - y = 11\\)\
\\(11x - y = 12\\)\
\\(11x + y = -12\\)

Explanation:

Step1: Find the slope (m)

We have two points \((x_1, y_1)=(4, 32)\) and \((x_2, y_2)=(6, 54)\). The slope formula is \(m = \frac{y_2 - y_1}{x_2 - x_1}\).
So, \(m=\frac{54 - 32}{6 - 4}=\frac{22}{2}=11\).

Step2: Use point - slope form \(y - y_1=m(x - x_1)\)

Using the point \((4, 32)\) and \(m = 11\), we get:
\(y-32 = 11(x - 4)\)

Step3: Simplify to slope - intercept form \(y=mx + b\)

Expand the right - hand side: \(y-32=11x-44\)
Add 32 to both sides: \(y=11x-44 + 32\), so \(y=11x-12\)

Step4: Convert to standard form \(Ax+By = C\) (where \(A\), \(B\), \(C\) are integers and \(A\geq0\))

Subtract \(11x\) from both sides: \(- 11x+y=-12\), multiply both sides by - 1 to make the coefficient of \(x\) positive: \(11x - y=12\)

Answer:

\(11x - y = 12\) (the option with "11x - y = 12")