Question

question
put the following equation of a line into slope - intercept form, simplifying all fractions.
12y - 15x = 84
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Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. We need to solve the given equation \(12y-15x = 84\) for \(y\).

Step2: Isolate the term with \(y\)

Add \(15x\) to both sides of the equation \(12y-15x=84\).
We get \(12y=15x + 84\).

Step3: Solve for \(y\)

Divide each term in the equation \(12y = 15x+84\) by \(12\).
\(y=\frac{15x}{12}+\frac{84}{12}\)

Step4: Simplify the fractions

Simplify \(\frac{15}{12}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 3. So \(\frac{15\div3}{12\div3}=\frac{5}{4}\).
Simplify \(\frac{84}{12}\) by dividing both the numerator and the denominator by 12. \(84\div12 = 7\).

So the equation in slope - intercept form is \(y=\frac{5}{4}x + 7\).

Answer:

\(y=\frac{5}{4}x + 7\)