Which equation in slope-intercept form is equivalent to y−1=−

Question

3
1
​
(x−6)?

y=−
3
1
​
x+5

None of these

y=
3
1
​
x−7

y=−
3
1
​
x+3

Answer 1

To start, let's convert the equation given in point-slope form \( y - 1 = -\frac{3}{1}(x - 6) \) into slope-intercept form.

1. Distribute the slope \(-\frac{3}{1}\) (which is \(-3\)) on the right side: \[ y - 1 = -3(x - 6) \] \[ y - 1 = -3x + 18 \]

2. Now, add \(1\) to both sides to isolate \(y\): \[ y = -3x + 18 + 1 \] \[ y = -3x + 19 \]

Now that we have the slope-intercept form \( y = -3x + 19 \), let's compare this with the given options:

1. \( y = -\frac{3}{1}x + 5 \) (This is incorrect because the constant term does not match)
2. None of these
3. \( y = \frac{3}{1}x - 7 \) (This is incorrect because both the slope and the constant term do not match)
4. \( y = -\frac{3}{1}x + 3 \) (This is incorrect because the constant term does not match)

Since none of the provided options match our derived equation \( y = -3x + 19 \), the correct answer is: None of these.