Which equation in slope-intercept form is equivalent to y−2=−

Question

4
3
​
(x−6)?

y=−
4
3
​
x+
2
13
​


None of these

y=−
4
3
​
x−4

y=−
4
3
​
x−8

Answer 1

To convert the equation \(y - 2 = -\frac{4}{3}(x - 6)\) into slope-intercept form (\(y = mx + b\)), we can follow these steps:

1. Distribute \(-\frac{4}{3}\) on the right side:

   \[ y - 2 = -\frac{4}{3}x + \frac{4}{3} \cdot 6 \]

   Calculating \(\frac{4}{3} \cdot 6\):

   \[ \frac{4}{3} \cdot 6 = \frac{24}{3} = 8 \]

   So now, we have:

   \[ y - 2 = -\frac{4}{3}x + 8 \]

2. Add \(2\) to both sides to solve for \(y\):

   \[ y = -\frac{4}{3}x + 8 + 2 \]

   This simplifies to:

   \[ y = -\frac{4}{3}x + 10 \]

Now we have the equation in slope-intercept form:

\[ y = -\frac{4}{3}x + 10 \]

Looking at the answer choices provided:

1. \(y = -\frac{4}{3}x + \frac{2}{13}\)
2. None of these
3. \(y = -\frac{4}{3}x - 4\)
4. \(y = -\frac{4}{3}x - 8\)

None of these options matches \(y = -\frac{4}{3}x + 10\). Therefore, the answer is:

None of these.