Which equation in slope-intercept form is equivalent to y−8=−

Question

2
3
​
(x+2)?

None of these.

y=−
3
2
​
x+10

y=−
2
3
​
x−5

y=
2
3
​
x+5

Answer 1

To convert the equation \(y - 8 = -\frac{2}{3}(x + 2)\) into slope-intercept form (which is \(y = mx + b\)), we can follow these steps:

1. Distribute the \(-\frac{2}{3}\) on the right side of the equation: \[ y - 8 = -\frac{2}{3}x - \frac{2}{3} \cdot 2 \] \[ y - 8 = -\frac{2}{3}x - \frac{4}{3} \]

2. Add 8 to both sides to solve for \(y\): \[ y = -\frac{2}{3}x - \frac{4}{3} + 8 \]

3. Convert 8 to a fraction with a denominator of 3: \[ 8 = \frac{24}{3} \]

4. Combine the constants: \[ y = -\frac{2}{3}x - \frac{4}{3} + \frac{24}{3} \] \[ y = -\frac{2}{3}x + \frac{20}{3} \]

Now that we have \(y = -\frac{2}{3}x + \frac{20}{3}\), let's analyze the options given to find the equivalent slope-intercept form:

• \(y=\frac{2}{3}x + 5\) (not equivalent)
• \(y=-\frac{2}{3}x - 5\) (not equivalent)
• \(y=-\frac{3}{2}x + 10\) (not equivalent)

None of these match our derived equation. Therefore, the correct answer is:

None of these.