Which equation in slope-intercept form is equivalent to y−3=−

Question

2
5
​
(x−5)?

y=−
2
5
​
x+
2
31
​


y=−
2
5
​
x−8

y=−
2
5
​
x+
2
19
​


None of these

Answer 1

To convert the equation \( y - 3 = -\frac{2}{5}(x - 5) \) into slope-intercept form (\( y = mx + b \)), we need to distribute and then isolate \( y \).

1. Distribute \( -\frac{2}{5} \) on the right side:

   \[ y - 3 = -\frac{2}{5}x + \frac{2}{5} \cdot 5 \] \[ y - 3 = -\frac{2}{5}x + 2 \]

2. Next, we add 3 to both sides to isolate \( y \):

   \[ y = -\frac{2}{5}x + 2 + 3 \] \[ y = -\frac{2}{5}x + 5 \]

Now we have the equation in slope-intercept form:

\[ y = -\frac{2}{5}x + 5 \]

Comparing this with the options given:

• \( y = -\frac{2}{5} x + \frac{231}{100} \) (not correct)
• \( y = -\frac{2}{5} x - 8 \) (not correct)
• \( y = -\frac{2}{5} x + \frac{219}{100} \) (not correct)
• None of these (correct option)

Thus, the answer is None of these.