Question

If a line can be represented by the equation y+2= 1/3 (x−12), which of the following sets of points lies on the line?

Answer 1

To determine which set of points lies on the line represented by the equation \( y + 2 = \frac{1}{3}(x - 12) \), we first need to rearrange this equation into the slope-intercept form \( y = mx + b \).

1. **Rearranging the equation:**

Start with \( y + 2 = \frac{1}{3}(x - 12) \).

Distributing the \( \frac{1}{3} \):
\[
y + 2 = \frac{1}{3}x - 4
\]

Subtracting 2 from both sides:
\[
y = \frac{1}{3}x - 4 - 2
\]
\[
y = \frac{1}{3}x - 6
\]

Now the equation of the line in slope-intercept form is \( y = \frac{1}{3}x - 6 \).

2. **Testing the points:**

To determine whether specific points lie on the line, you can plug in the x-values from each point into the equation \( y = \frac{1}{3}x - 6 \) and check if the resulting y-value matches the y-value of the point.

If you provide the set of points you want to test, I'll help you check each one!