Do the equations y−10.25=

Question

2
1
​
(x+3) and y−16.75=
2
1
​
(x−10) represent the same line?

No, because they both convert to different equations in slope-intercept form.

No. They cannot possibly represent the same line because they have different slopes.

Yes, because they both convert to y=
2
1
​
x+13.25 in slope-intercept form.

Yes, because they both convert to y=
2
1
​
x+11.75 in slope-intercept form.

Answer 1

To determine whether the two equations represent the same line, let's convert them to slope-intercept form (y = mx + b).

1. First equation: \[ y - 10.25 = \frac{2}{1}(x + 3) \] Simplifying this: \[ y - 10.25 = 2(x + 3) \] \[ y - 10.25 = 2x + 6 \] \[ y = 2x + 6 + 10.25 \] \[ y = 2x + 16.25 \]

2. Second equation: \[ y - 16.75 = \frac{2}{1}(x - 10) \] Simplifying this: \[ y - 16.75 = 2(x - 10) \] \[ y - 16.75 = 2x - 20 \] \[ y = 2x - 20 + 16.75 \] \[ y = 2x - 3.25 \]

Now we can compare the two slope-intercept forms:

• The first equation simplifies to \( y = 2x + 16.25 \).
• The second equation simplifies to \( y = 2x - 3.25 \).

Conclusion:

Both equations have the same slope (2) but different y-intercepts (16.25 and -3.25). Therefore, they represent different lines.

So the correct answer is: No, because they both convert to different equations in slope-intercept form.